When they were students at the New Orleans Center for Creative Arts, Jon Batiste and Troy “Trombone Shorty” Andrews formed a band called Orleans Avenue. Andrews still leads Orleans Avenue, which now fills concert venues around the globe, and will close the New Orleans Jazz & Heritage Festival’s main Acura Stage on Sunday.

Batiste left Orleans Avenue at age 17 to move to New York City and enroll at the prestigious Juilliard School. Quitting a band that became one of New Orleans’ most successful musical exports of the past 20 years does not, on paper, sound like a smart career move.

But Batiste has done just fine.

Every weeknight, he and Stay Human, the band he built with fellow Juilliard students, are seen by millions of viewers of “The Late Show with Stephen Colbert” on CBS.

The 29-year-old Batiste, like predecessor Paul Shaffer when David Letterman was the show’s star, serves as the host’s bandleader and foil, receiving plenty of air time even when he’s not playing music.

Batiste has a five-year contract with “The Late Show,” the “longest term that I’ve ever been signed on to do anything,” he said Thursday, calling from the Ed Sullivan Theater after rehearsals for the first of two shows he’d tape that day. “For a musician to have a regular, full-time job for that amount of time is rare these days.”

Aside from the advantages of the lucrative job itself, the nightly national TV exposure has made Batiste and Stay Human far more marketable for their own shows and albums.

They’ll return to his hometown for a performance at 1:40 p.m. Saturday (April 30) at Jazz Fest’s Acura Stage. Later in the day, Batiste and Stay Human will headline a show at the Civic Theater. Guitarist Benjamin Booker is also on the bill. Show time is 10 p.m.

Before “The Late Show” launched in September, Batiste and Stay Human had already established themselves as a free-ranging, jazz-based unit that revels in highly participatory, unconventional concerts. Armed with his trademark melodica — a toy piano that requires the user to blow air into it — he loves to break down the barrier between performer and audience.

TV has opened up a whole set of opportunities, along with the sort of financial stability that jazz musicians rarely achieve.

When his contract runs out, “we’ll have a lot more perspective” on what the job can be, he said. “But the way things are going now, it seems like something that is great. I don’t see us stopping anytime soon.”

A musician by birth

Batiste was a musician by birth. His family lineage in New Orleans goes back generations. His father, uncles and other relatives formed the Batiste Brothers Band, which trafficked in a distinctly local brand of funk and soul.

Young Jonathan’s first stage experience was sitting in on percussion with the Batiste Brothers as a child. He transitioned to piano, and his prodigious talent bloomed at NOCCA.

He still leans on the lessons he learned at NOCCA — which he described as “like a college program for high school” — and from his family.

“There’s nothing that can really prepare you like having a good teacher,” he said. “I feel like I had a head start growing up in New Orleans with who my family is, and the experiences that I had very early on with the business. And also just learning about how to experience music in a way that brings people in, and is joyous and uplifting but still on a very, very high level of virtuosity.”

At Juilliard, he was surrounded by musicians as talented as he was. He took up the melodica — which many of his teachers did not consider to be an instrument worthy of those hallowed halls — in 2011, soon afterward forming Stay Human while working toward a master’s degree.

After classes at Juilliard, he and his bandmates would perform for passersby on New York subway platforms.

The melodica’s mobility has certain practical advantages.

“I started playing it because you can’t take a piano down in the subway,” he said. “We wanted to figure out how to take our sound and create music anywhere we went. The melodica has a character, and it’s a special sound that almost has the influence of zydeco music. My grandfather loved zydeco music, so it has a special place in my heart.”

Stay Human released a couple of albums and made memorable appearances at the Bonnaroo festival, Carnegie Hall and other venues. They spent nine months on tour between 2013 and 2014.

Batiste also started landing TV gigs. He played himself on several episodes of the New Orleans-set HBO series “Treme.”

In 2014, he appeared on “The Colbert Report,” the Comedy Central show that made Stephen Colbert a star and paved the way for him to take over Letterman’s job at “The Late Show.” Batiste made an impression on the host, especially when he led the studio audience out onto the street.

Lobbying for a job

Batiste was invited back as one of dozens of special guests for Colbert’s farewell “Colbert Report.” He made a concerted effort to land the bandleader gig for “The Late Show.” He did his homework, even arranging a lunch with Shaffer to pick the veteran musician’s brain. During multiple conversations with Colbert, Batiste pitched his ideas.

He was in St. Louis for a concert when Colbert called to offer him the gig. The host traveled to New Orleans and filmed a clip at the Blue Nile on Frenchmen Street — it involved a plate of beignets and lots of powdered sugar — to announce Batiste’s hiring.

“We didn’t know what to expect from looking at the older shows, like David Letterman and Johnny Carson,” Batiste said. “You get an idea of what the format is, but everybody makes it their own. Stephen had his own vision. I thought about how do I fit into that vision beforehand. When we get on set, that’s when it really comes to life.”

Seven months in, “everybody is still excited about it. It still feels new, and the energy is flowing.”

Taping five hourlong shows a week and learning new music constantly is a grind. “You’ve got to learn how to pace it,” Batiste said. “The energy level that you bring to the show requires 110 percent, so you’re drained afterward. It’s a matter of what you do in the time that you’re not on set, and how do you balance it so that you can get that energy when you are on set.

“We’re taking this first year to get used to what we’re doing, and understand how it affects us mentally and physically.”

Colbert calls on Batiste frequently during shows. The day Prince died, Colbert prompted Batiste to talk about sitting in with Prince’s band a couple of times.

It’s likely Batiste and company will salute Prince at Jazz Fest and the Civic. They are eager to play somewhere other than the Ed Sullivan Theater, even if they’ve got only an hour onstage at Jazz Fest.

“That’s a lot more than what we’ve been doing for the last seven months” on “The Late Show,” Batiste said. “A TV show is more structured than a live gig will ever be.”

Bringing N.O. to the world

Just as his buddy Andrews has done wonders for the trombone’s reputation, Batiste is out to make the melodica hip. “That’s one of the cool things about that instrument: It’s a child’s toy, but it depends on who’s playing it,” he said.

He’s happy that both he and Andrews, childhood classmates and bandmates, have gone on to bigger and better things.

“He’s like one of my brothers,” Batiste said. “He’s doing some great stuff. We run into each other every now and then on the road. It’s cool to see how we’re both out here representing New Orleans music.

“We had a good time at NOCCA. Now we’re bringing it to the rest of the world.”