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

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 voluntarily leave elite programs, and created enticing vacancies at the universities Riley and Kelly left behind.

Kelly had seemed like an institution at Notre Dame after 12 years in the top job, including a national championship game appearance after 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.)

The Fighting Irish finished the regular season 11-1 this year but may need a loss by a top team to earn a berth in the national championship playoff. Notre Dame was ranked sixth in the most recent rankings for the four-team playoff. The new rankings will be released on Tuesday night.

Earlier this season, Kelly surpassed Knute Rockne to be Notre Dame’s winningest coach of all time. But his résumé lacks a major bowl victory, with losses in the Fiesta, Cotton and Rose Bowls along with the national championship game loss.

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.

Although no official salary figures were reported, multiple news reports said Kelly would be paid between $10 million and $15 million a year at L.S.U., a significant increase from a salary believed to be in the $3 million range at Notre Dame.

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.