Brian Kelly will leave Notre Dame to become the football coach at Louisiana State, the latest in a series of changes at some of the country’s most storied college football programs.

The news was confirmed Tuesday morning by L.S.U.

The hiring follows the move of Lincoln Riley from Oklahoma to Southern California. Both shifts surprised the college football world, where coaches do not regularly leave elite programs voluntarily, and created enticing vacancies at the universities Riley and Kelly left behind.

The Fighting Irish finished the regular season 11-1 this year and, if a top team loses, could earn a berth in the College Football Playoff. Notre Dame was ranked sixth in the most recent rankings for the four-team playoff released on Tuesday night. Georgia, Michigan, Alabama and Cincinnati were the top four teams, and Oklahoma came in at 14th.

Kelly had seemed like an institution at Notre Dame after 12 years in the top job. He had a national championship game appearance in the 2012 season and a 113-40 overall record. (The wins in the championship game season were later vacated by the N.C.A.A. after a trainer was found to have done coursework for players.) This season, Kelly surpassed Knute Rockne with the most wins as a coach for the university.

As unusual as it is for a head coach with Kelly’s success to leave a program that is still in the playoff hunt, his move could potentially position him to finally win a national championship, something he could not do at Notre Dame. Kelly lacks a top-tier bowl victory, with losses in the Fiesta, Cotton and Rose Bowls, along with the national championship game loss.

And Notre Dame, despite Kelly’s elite recruiting (he has produced a top-20 class every season since taking over the head coaching job in 2010), appeared severely outmatched in its recent playoff appearances, losing to Alabama and Clemson by a combined 44 points.

Louisiana has one of the most ripe recruiting grounds in the country. L.S.U. has had a class outside the top 10 only twice since 2010. Kelly will have access to as much talent as he has seen.

L.S.U. won the national championship after the 2019 season, only to fall to 5-5 in 2020. Coach Ed Orgeron announced this would be his last season in October, when his team was 4-3. The Tigers currently stand 6-6. Like his predecessor, Les Miles, he found that not even a national title guaranteed long-term job security in Baton Rouge.

L.S.U. reported that Kelly would be paid $95 million over 10 years, plus incentives, a significant increase from a salary believed to be in the $3 million range at Notre Dame.

“I could not be more excited to join a program with the commitment to excellence, rich traditions, and unrivaled pride and passion,” Kelly said in a statement that L.S.U. released Tuesday morning. He added: “I am fully committed to recruiting, developing, and graduating elite student-athletes, winning championships, and working together with our administration to make Louisiana proud. Our potential is unlimited, and I cannot wait to call Baton Rouge home.”

Scott Woodward, the university’s athletic director, called Kelly “the epitome of a winner.”

Reports had initially linked L.S.U. with Riley, who over the weekend denied he would take the job before he moved to U.S.C. There also had been in-state support for the University of Louisiana coach Billy Napier, but he chose to go to Florida.

Luring Kelly from Notre Dame, though, was an even bigger surprise.

Kelly started his career at Grand Valley State in Michigan, where he won two Division II national titles. He then spent three years at Central Michigan and four at Cincinnati, culminating in an undefeated regular season. That landed him the Notre Dame job.

The hiring of Kelly at L.S.U. helps keep the Southeastern Conference at the center of the college football universe: The conference has recently added the powerhouse teams Texas and Oklahoma, and its members Alabama and L.S.U. have won four of the seven national championships in the playoff era.

Another Southeastern Conference team, Georgia, is undefeated and No. 1 in the country this year. It will face Alabama (11-1), third in the playoff rankings, in the conference championship game on Saturday in Atlanta.

Alan Blinder and Alanis Thames contributed reporting.