After not playing in a conference championship game, the Buckeyes (11-1) moved up one spot following USC's loss in the Pac-12 title game Friday to give the Big Ten two playoff teams for the first time in the format's nine-year history.
"How we got here, at this point, I guess doesn't really matter now that we're here," Ohio State coach Ryan Day said.
No. 4 Ohio State will face No. 1 Georgia in the Chick-fil-A Peach Bowl, and No. 2 Michigan will face No. 3 TCU in the Vrbo Fiesta Bowl on Dec. 31.
The CFP National Championship presented by AT&T will be played Jan. 9 at SoFi Stadium in Inglewood, California.
TCU (12-1) held on to its No. 3 ranking after losing in overtime in the Big 12 championship game to Kansas State. The Horned Frogs and Buckeyes are the fifth and sixth teams to make the College Football Playoff without winning a conference title.
Horned Frogs coach Sonny Dykes said he was concerned about his team's playoff status after the loss but added that he had faith in the selection committee.
At a watch party for TCU players and staffers at its Fort Worth, Texas, campus, cheers broke out when the Frogs landed in the bracket during the announcement show.
"We had a little bit of a sleepless night, but appreciate the committee's confidence in our players and our program," Dykes said Sunday. "I think it's all you can ask for at the beginning of the season."
Alabama (10-2) had hoped to make a jump into the top four following USC's and TCU's losses, with coach Nick Saban lobbying for his team Saturday.
"If we played any of those teams that are on the edge of getting in, would we be the underdogs or the favorite?" Saban said on Fox at halftime of the Big Ten championship.
The Crimson Tide were ranked fifth by the selection committee.
"As we looked at the total body of work, the committee was comfortable with Ohio State at No. 4 and Alabama at 5," Corrigan said in an interview on ESPN.
Corrigan also told ESPN's Heather Dinich that potentially having three teams (TCU, Alabama and Ohio State) without conference titles changed the conversation some in the room as they debated the merits of each.
"Obviously it's going to change some because it's different than what it's been in the past," he said, "but our goal is to look at the totality of the games that are played."
Corrigan said there was significant discussion around Alabama, but without conference titles, more consideration was given to résumés. TCU's regular-season win over Kansas State loomed large in the final decision -- the committee was impressed by the Horned Frogs' comeback and 10-point victory margin -- but Corrigan said that was only one example of what impressed the committee.
"You think about TCU in the game against Baylor, getting on the field, running on the field, kicking the field goal speaks to a disciplined team, a well-rounded team," he said. "We're trying to look at everything we can as we go into this."
Georgia (13-0) and Michigan (13-0) are in the playoff for the second straight year. They won their respective conference title games handily Saturday and will look to become the fourth team to win the CFP with an undefeated record.
The only time Georgia and Ohio State have previously played was in the 1992 Citrus Bowl, a 21-14 Bulldogs victory. TCU, whose only national title came in 1938, has never played Michigan.
The Wolverines had plenty of praise for their semifinal opponent after a number of players watched Saturday's Big 12 championship game.
"Max Duggan, he's a great player," Michigan quarterback J.J. McCarthy said, "but it will be awesome to see how he shapes up against our defense. I always look at other quarterbacks to see if I can take bits and pieces from their game and add it to mine. Max, he's a tough dude. Seeing him run the ball, especially on those last couple of drives, it was really standing out and realizing, 'Hey, it's Big 12, but there will be opportunity for me to use my legs.'"
Michigan also wants to take another step forward after reaching the semifinals last season before being blown out by Georgia.
"That ultimate goal, we really weren't shooting for that national championship last year," McCarthy said. "It was to beat Ohio State, win a Big Ten championship, but this year, we're shooting for it, and we're going to go get it."
Corrigan said the committee did not make any special effort to avoid having a rematch of Ohio State and Michigan in a semifinal. The Buckeyes and Wolverines have never played outside of their annual regular-season game in a rivalry that dates back to 1902.
ESPN's Adam Rittenberg and The Associated Press contributed to this report.