For singer-songwriter Maggie Rogers, playing two sold-out shows at Radio City Music Hall on Tuesday and Wednesday will be a real full-circle moment: Three years ago at the venue, she performed “Alaska” — a song off her major-label debut album, “Heard It in a Past Life” — at her graduation from New York University’s Clive Davis Institute of Recorded Music.

“It all sort of leads up to this moment at Radio City,” says Rogers, 25, of her post-NYU musical journey. “I made a promise to myself that I would try and get [back] there within 10 years, so to be back there three years later with two sold-out nights, it’s so bizarre to me. [This is] the realm of dreams you don’t say out loud.”

Rogers has been on a wild ride ever since she was the musical guest on “Saturday Night Live” in November — on the same day she found out about getting booked at Radio City. That was two months before “Heard It in a Past Life” — an eclectic mix of pop, folk and electronica, with shades of R&B and hip-hop — even came out, debuting at No. 2 on the Billboard albums chart. “The alignment for all of this has been so ridiculous,” she says.

The stars started to line up for this artist when she began playing the harp at 7 while growing up in Easton, Maryland. After listening to neo-soul artists such as Erykah Badu and Lauryn Hill whom her mom played on the way to her classical music lessons, Rogers picked up the piano and guitar in middle school, then branched into the banjo and folk-bluegrass music in high school.

The demos for “Echo” — which she released in high school as the first of her two independent albums — helped Rogers get into the Clive Davis Institute. But she got a different kind of musical education on the streets of New York.

“I grew up in a really rural area, where I had to beg an adult to drive me two to three hours each way to see a concert,” she says. “And so at 18, I got to move to New York City and suddenly see as much live music as I wanted. I was going uptown to salsa clubs, I was going to poetry readings at the Nuyorican [Poets Cafe], I was going to see hip-hop open mikes in Bushwick, I was going to see punk shows. I just gorged myself on live music.”

A couple months before her NYU graduation, Rogers got her big break when Pharrell Williams was a guest speaker during a master class and was deeply moved by her performance of “Alaska.” The video capturing that moment went viral.

“I had no idea that Pharrell was coming to class that day,” she says. “It was just my day to share work. And ‘Alaska’ was the first song I had written in two and a half years. I had gone through a long period of writer’s block and sort of had to start writing because I needed to graduate.”

Rogers’ bond with Mr. “Happy” didn’t end there: “Pharrell called me when my record came out and congratulated me. It’s funny that I now have this eternal tie with this person.”

While she made a “full commitment to living on a tour bus for the last two and a half years,” leaving most of her stuff in boxes at her parents’ home in Maryland, Rogers says she will always have a special connection to the Big Apple. “New York always still feels like my home,” she says. “New York has my heart.”

As her tour winds down this fall, Rogers is also generating Grammy buzz, looking like a strong contender for a Best New Artist nomination. “If the Grammys happened, that’d be supercool and I would call my mom,” she says. “But they’re also out of my control. The Grammys recognize achievement, but that achievement for me is recognized every night [onstage].”

Whatever her Grammy fate is, Rogers believes that all of her past lives have led up to her success now. “I think when these great events happen in our lives, we find ways to explain them to ourselves,” she says. “And the way that made the most sense to me was that I had just been trying to do this for a lot of lifetimes, and this is the one where it all lines up.”