The potential for chaos gave way to consensus: Louisiana State, Ohio State, Clemson and Oklahoma will compete for a national title after their selections on Sunday for the College Football Playoff.

The season’s semifinalists, announced after the conference championship games and deliberations by a 13-member committee, made official that the playoff would include a trio of undefeated teams for a second straight year. And with a host of blue-chip programs damaged by at least two losses each, the committee’s picks also appeared more immune than usual from the bickering that has so often surrounded college football’s postseason.

Louisiana State, which overtook Ohio State for the top spot in the rankings on Sunday, will meet No. 4 Oklahoma in the Peach Bowl in Atlanta on Dec. 28. No. 2 Ohio State and third-ranked Clemson will play in the Fiesta Bowl, near Phoenix, later that day. The winners of the semifinal matchups will advance to the national championship game, scheduled for Jan. 13 in New Orleans.

“Obviously it’s an accomplishment, but it’s not our final destination,” said Ed Orgeron, the coach at L.S.U., after the committee announced that his team would make its inaugural appearance in the four-team playoff.