“Congratulations for making it here,” Nézet-Séguin told what was left of the audience. “You’ve officially earned the title of ‘die-hard fans of the Philadelphia Orchestra.’ ” His tone was cheerful. His Québécois-accented English made it clear he’s not local, but, as he does with audiences, he quickly put this one at ease. The day after this snow-crossed concert, Nézet-Séguin would celebrate his 40th birthday, though he is a compact, wide-eyed man who looks 10 years younger.

The Montrealer is fast becoming one of the most powerful and influential classical musicians in the world. He has appeared at the head of most of the world’s leading orchestras and opera companies. He sells out halls in Salzburg, Paris and New York. His recording contract with Deutsche Grammophon is open-ended, allowing him to record a wide variety of works with an assortment of orchestras at a time when few conductors have any recording contract at all. The Financial Times has called him “the greatest generator of energy on the international podium.” He is regarded as a saviour for the legendary Philadelphia Orchestra, which emerged from bankruptcy protection in 2012 and is now playing to full houses consistently for the first time in decades. But he is so unassuming, the reasons for his success are hardly obvious when he does not have a baton in one hand and 100 superbly trained musicians responding to his every gesture.

This particular day had been organizational chaos. As a rule, North American orchestras rehearse each week’s 90-minute program for three days, then perform it on successive nights. This week’s final rehearsal was to have been earlier that day, but, as the snow piled up, the rehearsal was postponed, then cancelled. The truncated practice time and absent musicians meant the evening’s main work, Vaughan Williams’s dark and difficult Fourth Symphony, couldn’t be played. In its place, Nézet-Séguin announced he would share a piano bench with the guest soloist, the great pianist Emanuel Ax, and play Ravel’s Mother Goose suite as a set of single-keyboard duets. At this news, many in the crowd gasped in delight.

This is Nézet-Séguin’s third season as music director of the Philadelphia Orchestra and, by now, its audiences will happily embrace any move he makes. Piano duets might seem a pale substitute for a full symphony, but the crowd embraced the chance to see their man operating at a different, more intimate scale. The duets were charming. When Ax returned later for Beethoven’s Third Piano Concerto, Nézet-Séguin led the orchestra in his accustomed style, conducting with his whole body, conveying both the broad sweep of the music and innumerable smaller details. No show-off, despite his expressiveness, he favours rich texture over cheap fireworks.

Philadelphia was home to legendary conductors for decades—Leopold Stokowski, Eugene Ormandy, Riccardo Muti—and, for all his lack of fuss, there is something larger-than-life about Nézet-Séguin’s stage persona that allows him to fit into that lineage. A photograph of his face, blown up to barn-door size and plastered on a billboard, greets visitors to the Kimmel Centre. Next to it, a florid quotation from Nézet-Séguin is transcribed: “The Philadelphia Orchestra may travel the world, but it is you, our beloved Philadelphia audience, that makes it possible for us to create the great Philadelphia Sound . . . This is our home. First and foremost, we play for you.”

That news might surprise audiences in Montreal, who have known Nézet-Seguin as artistic director of the Orchestre Métropolitain for 15 years, or in the Netherlands, where he has been principal conductor of the Rotterdam Philharmonic since 2008. But there are layers of truth to the billboard copy that help to explain why Yannick Nézet-Séguin, an unassuming Montrealer, has become one of the leading forces in classical music.

First, it’s hardly unusual for a conductor to divide his time among leading roles with more than one ensemble. An orchestra season is a combination of performances with a chief conductor or music director, and performances with a series of travelling guest conductors. Nézet-Séguin has three “home” ensembles, and takes relatively few one-week guest assignments elsewhere.

Second, part of his extraordinary success is his ability to find long moments of serenity and focus within the jet-setting schedule of a modern concert star. “When we appointed Yannick, we appointed Yannick, Pierre, Serge and Claudine,” Allison Vulgamore, the Philadelphia Orchestra’s president and chief executive officer, told me. She was referring to his father, Serge Séguin, and his mother, Claudine Nézet, who help to manage his career, and his partner, Montreal violist Pierre Tourville. “It is very much a family affair here. They’re almost always here.” They are also almost always in Montreal, and often in Rotterdam. “He has some ability,” Vulgamore said, “to be wholly present wherever he is.”

The same is true in music. Whatever he conducts seems to be the most important music to him while he is conducting it, his collaborators the greatest he has known for as long as they are together. Musicians in Philadelphia still talk about the night, two years ago, when Nézet-Séguin was palpably delighted to share the stage with actor Hugh Jackman for a gala benefit concert. (“Remember the name, ladies and gentlemen,” Jackman said of his diminutive host. “It’s worth 600 points in Scrabble!”) Other conductors sometimes begrudge these forced departures from the serious task of leading a serious ensemble. Nézet-Séguin had a blast.

It happened again in January, when he led the orchestra in a free concert to celebrate the legacy of Martin Luther King Jr. The concert featured a performance of a new piece for orchestra and chorus by Hannibal, a composer and jazz trumpeter who used to perform under his given name, Marvin Peterson. There is little in Nézet-Séguin’s background to suggest he’d fit into a celebration of African-American culture, but when the concert was over, Hannibal hugged Nézet-Séguin so fiercely, the young Montrealer’s feet kicked as they left the ground.

His ability to transform any performance space into Nézet-Séguin space means that memorable moments follow him into unlikely venues. For 15 years, he has led the Orchestre Métropolitain on frequent tours through the city’s residential neighbourhoods, funded by the Conseil des Arts de Montréal. The venues are often ramshackle, the audiences casually dressed and, until Nézet-Séguin became its guiding force at the age of 25, nobody would have counted the Orchestre Métropolitain as a particularly distinguished orchestra.

But in 2009, I watched him lead the Métropolitain and two vocal soloists in a performance of Mahler’s Das Lied von der Erde, in a smelly college auditorium near the east-end Olympic stadium, that stands as one of the great concert experiences of my life. After the last notes died away, Nézet-Séguin held his baton aloft for nearly a minute amid awed silence. Nobody in the audience made a sound. Even after he dropped his arm, the crowd withheld its reaction, until finally he tossed his baton onto the ledge of his music stand. Then the applause was torrential.

None of the musicians I spoke to for this article would say a word against him. “It’s quite the love affair at the moment,” Jennifer Montone, Philadelphia’s principal French horn player, told me. “He’s everything that we need, and he’s just incredibly genuine, he’s very intelligent. He has exceeded every expectation that any of us had.”

How does a musician garner that kind of respect? A conductor stands between a composer, who conceived the work, and players, who have spent their lives making the music come back to life. The worst conductors simply get in the way of that relationship. The better ones can be temperamental, imperious, or only intermittently successful in adding the interpretive insight that allows them to elevate a performance beyond the routine. The dashed hopes of a hundred speed-dating disasters, with guests whose reputations or egos outstrips their ability, make orchestra musicians a notoriously tough crowd, but Nézet-Séguin conquers every orchestra he meets. “He comes, he conducts, he is invited back,” the New York Times said in 2009, on the eve of the Montrealer’s first appearance as a guest conductor at the Metropolitan Opera.

How does any conductor earn such authority, particularly one so diminutive and soft-spoken? (In three seasons, he has appeared to lose his temper only once, and only mildly, Philadelphia bassist David Fay told me. He promptly apologized to the musicians for the fleeting outburst, an almost unheard-of gesture.)

“This is a question I had to ask myself very early on, of course, because I did start very early,” Nézet-Séguin told me during a thoughtful and wide-ranging pre-concert interview in his Kimmel Centre dressing room. “Authority. Respect. What are these concepts? . . . When I was first on the podium, I was very nervous. But then I was thinking, ‘OK, what can I bring that I can bring, which I can’t pretend to? I can’t pretend to have experience. I can’t pretend to have age or reputation. So what is the thing that is not attackable?’

“There are two things. [One is] the quality of the preparation. I can know my scores better than anyone. This, I can control. I can spend a million hours really studying the score and being absolutely unattackable on that front. And the other thing, which I always had, was the love of music that I could share.”

There is one more sense in which he plays “first and foremost” for Philadelphia audiences. His accomplishments in Montreal are formidable, but the Métropolitain will always be that city’s second orchestra. The Orchestre symphonique de Montréal, under Kent Nagano, plays more often, has more money, and will always have a higher profile. Nézet-Séguin doesn’t rule out projects with the larger orchestra, but he says loyalty will forever keep him from leaving the Métropolitain for the OSM. The Rotterdam Philharmonic has a similar kid-brother relationship to Amsterdam’s Concertgebouw orchestra an hour’s drive away. Only Philadelphia, resurgent after a decade of financial turbulence, is the king of its castle. It was the orchestra Leopold Stokowski conducted in Walt Disney’s Fantasia. Three times a year, its members crowd into a special two-car train for the short ride to New York, where they reliably bring the house down at Carnegie Hall. Only in Philadelphia does his current post put him at the very centre of a great city’s cultural life.

That’s all the more true because American orchestras depend heavily on private sector fundraising for the money that comes from government grants elsewhere. And so Nézet-Séguin has had to get up close and personal, fast, with Philadelphia’s philanthropists.

Perhaps inevitably, he has knocked this assignment, too, out of the park. Donations are higher than ever in the orchestra’s history, and this man who makes the most of any situation has found he adores the donor-circuit schmooze. “I have dinners and cocktails with the donors, but we only talk about music. I don’t talk money with them. I talk only about my passion for music. I listen to what they like, what they like less and, after that, I’m still sovereign in my choices. I find that this contact with our listeners is precious. I feel, even after three years in Philadelphia, more at the centre of the action than I could have felt after many years in Montreal. Now it’s true that in Montreal, there’s another orchestra there. I’m not alone. That may be what makes it feel like—even though I’m the local boy in Montreal—I’ll always be the local boy. I’m not complaining. But here, I feel like I’m at the centre of the action.”

In Montreal, “I still feel like the hope, the young guy who’s still young, who one day will become great. I think there will always be a perception in Montreal that I’m younger than I am.” The feeling of being underrated at home isn’t as strong as it once was, he added. “Now, for a few years, the Metropolitain has taken its place. I know I still have a lot to contribute in Montreal and, as long as I feel that I can contribute something, and that it gives me something musically, I’ll stay.”

His contract with Philadelphia runs through 2022. His contract with Montreal seems eternal. Does that mean he is closing the door on other prestige appointments? The Berlin Philharmonic will be without a music director after 2018. The New York Philharmonic and its neighbour, the Metropolitan Opera, are both looking for music directors.

Nézet-Séguin surprised me by answering my question categorically. “No, no, no. Closing the door to New York or Berlin? No, not at all. I think that in the years to come, I’ll continue in Philadelphia. It’ll be the centre of my activity.” As for Rotterdam, “It’s clear that I have fewer years left than I did when I started. And that’s fine, there’s a cycle there.” The implication is that when that contract ends in 2018, he will consider himself free to find a new home to complement Philadelphia and Montreal. Either New York or Berlin would be a great prize. Nézet-Séguin is already a valued guest in both locales.

The strongest impression in watching Nézet-Séguin revive a great orchestra, and in talking to his colleagues, is that his career pinnacle lies ahead, that he has not yet even hit cruising velocity. Classical music is full of prodigies who falter before their promise is fulfilled. But at 40, Nézet-Séguin’s ambition and ability are only growing. His career is becoming a testament to the power of preparation and love.