He is scheduled to be introduced at a news conference at noon ET on Sunday.
"I'm humbled and honored for the opportunity to be the head coach at Florida State University, one of the iconic brands in college football," Norvell said in a statement announcing his hiring. "I'm so very excited for the future and the opportunity to return Florida State football to one of the nation's elite. I'm looking forward to hitting the ground running, putting together a great signing class, a tremendous coaching staff and joining arms with our current and former players to help elevate our football program each and every day."
Norvell guided Memphis (12-1) to its first AAC title in its third straight conference championship game. Eight days after beating Cincinnati 34-24 at home in the regular-season finale, Memphis rallied for another win, 29-24, on Saturday.
The Tigers now wait for an invitation to the Cotton Bowl as the highest-ranked Group of 5 team.
The transformation of Memphis' program under Norvell has been stunning. The Tigers have won eight or more games for six straight seasons, and Norvell has been at the helm for the past four. From 1974 to 2013, the Tigers had just two seasons of eight or more wins.
One of the youngest head coaches in the country when he took over at Memphis, Norvell, 38, replaces Willie Taggart at Florida State. Taggart was fired nine games into his second season at FSU earlier this year. He was 9-12 in 21 games as FSU's coach.
Norvell becomes the second-youngest coach of a Power 5 school, after 36-year-old Lincoln Riley of Oklahoma.
"We are excited that our football program has attracted one of the finest coaches in the country," Florida State athletic director David Coburn said in the statement. "We had a list of criteria that our new head coach needed to meet that went well beyond his record, and Mike Norvell exceeded all of them. At the top of that list was attracting a coach who could lead the program back to competing for championships. We believe we have the coach to do that."
Despite his age, Norvell is one of the most respected offensive minds in college football. Memphis has set multiple school records on offense and scored 30 or more points in 43 of the 53 games of his tenure. Only Oklahoma and Ohio State have averaged more points per game in the four seasons that Norvell has coached the Tigers.
He was the offensive coordinator at Arizona State under Todd Graham before getting the Memphis job and before that worked under Graham at Pittsburgh as the co-offensive coordinator and at Tulsa as the passing game coordinator.
The Associated Press contributed to this report.