The choreographer and director Justin Peck, who first gained attention as a dancer at New York City Ballet, has worked with A-listers ranging from Steven Spielberg to Dolly Parton. Yet Mr. Peck identifies the generally lesser-known — if avidly admired — singer/songwriter Sufjan Stevens as “maybe the most important collaborator I’ve had in my career up to this point.” 

Mr. Peck’s creative relationship with Mr. Stevens began more than a dozen years ago, when the former, then in his early 20s, inquired about adapting the latter’s 2009 album “Run Rabbit Run” into a ballet. The latest project teaming the pair also began life as a recording, 2005’s cult classic “Illinois,” a collection of soaring, lushly orchestrated tunes touching on subjects ranging from zombies to superheroes, and from a UFO sighting to the serial killer John Wayne Gacy.

“Illinoise,” as the new piece is called, was staged at Bard College and at Chicago before having its premiere off-Broadway, at the Park Avenue Armory, to effusive praise in March. This Wednesday, less than a month after completing that run — and just a day before the cutoff for eligibility for this season’s Tony Awards — it is set to open Broadway’s St. James Theatre.

If, as many are now speculating, “Illinoise” emerges as a prominent contender for those and other honors, it won’t be Mr. Peck’s first time invited to the party: He won Tony and Drama Desk awards in 2018 for his first Broadway assignment, choreographing a revival of “Carousel.” That’s not to say he would take the added recognition for granted.

“I started as a theater kid,” Mr. Peck, who also provided new choreography for Mr. Spielberg’s 2021 screen adaptation of “West Side Story,” says. “Theater was really my entry not just into dance, but into the arts and culture in general. So I have this deep, deep love for the work that I was able to see on and off-Broadway as a young person; it’s informed a lot of the work I’ve done over the years, regardless of the medium.”

A hybrid of musical theater and dance, “Illinoise” features no spoken words; its story, which Mr. Peck constructed with a Pulitzer Prize-winning playwright, Jackie Sibblies Drury, is told through music and movement. Although anchored by one young man’s journey through love and loss, it weaves in tales by other “storytellers,” who between numbers commune in an intimate setting evoking a campfire gathering.

Mr. Peck admits it took “about four or five years” to get Mr. Stevens to consent to the project. “I can’t really speak on his behalf, but he’s not really a big musical theater person — the same way he wasn’t really a big dance or ballet person when we started working together at the New York City Ballet. It’s a process that requires patience, working with Sufjan, to build that trust. I think it’s been worth the wait.” 

Mr. Stevens’s own involvement in “Illinoise” has been limited: “Sufjan was very deliberate about giving his blessing and staying present in relation to how the music was going to be developed, under the hand of [arranger and orchestrator] Timo Andres, the person he felt was the one to adapt it for this purpose. Beyond that, Sufjan made a decision to stay hands off. I think the album has a lot of ghosts that he didn’t necessarily want to revisit; he’s also a very forward-thinking artist, always about moving onto the next thing.”

Like Mr. Peck, who discovered “Illinois” as a teenager, Ms. Drury, whose noted plays include “Fairview” and “Social Creatures,” was a fan of the album. “I listened to it a lot in my early 20s,” she says. Initially, though, she “couldn’t imagine how it could be turned into a musical. I think I had horrible visions of it in my head at first. But after seeing the work that Justin had already done and talking to him about his vision for the piece, I realized he had a deep reverence for it, and an understanding of how the music on the album was functioning.”

Ms. Drury, who is making her Broadway debut with “Illinoise,” did not start with the premise that there would be no dialogue. “But because there’s so much emotion in the movement and in the music itself, it felt like words would be superfluous,” she says. “There was so much clarity in the movement that Justin was creating that it felt like trying to describe it would be like putting a hat on a hat.”

The production is not undergoing any substantial changes in its transfer to Broadway, Mr. Peck says, “aside from making sure it adapts to the St. James. It’s more about moving to another space than starting over with another process. It’s the same group of musicians and almost entirely the same cast. The one exception is that one of the cast members of the original iteration, Brandt Martinez, is going into the role played at the Armory by Robbie Fairchild.” (Mr. Fairchild, a former City Ballet principal dancer who starred in Broadway’s “An American in Paris” nine years ago, had a schedule conflict.)

“I think that’s part of why moving so quickly made sense to us — because we knew it was an opportunity to preserve the cast,” Mr. Peck says. “We feel very strongly that this is the cast to be telling this story. So we’re thrilled about that.”

It’s not guaranteed that Mr. Stevens will catch “Illinoise” during its limited Broadway engagement, which ends August 10. “He hasn’t seen the show yet,” Mr. Peck notes. “But that has a lot to do with him having an extraordinarily difficult year. He lost his partner, and he’s been struggling with an auto-immune disease that has left him unable to walk.” (Mr. Stevens disclosed last year that he had been diagnosed with Guillain-Barré syndrome.) 

Mr. Peck and Ms. Drury are hopeful that the new production of “Illinoise” will remind fans of the vitality of Mr. Stevens’s work, while sharing their own inspiration.

“There were so many people who were trying to get to see the show in Chicago, and at the Armory, who weren’t able to see it,” Ms. Drury says. “So it’s really exciting for Justin and me, and for the entire cast and crew, that we get to share it with so many more people. That’s genuinely thrilling, for all of us.”