The first game will be held Sept. 15, 2018, at TCU's Amon G. Carter Stadium. The Horned Frogs will visit Ohio Stadium on Sept. 21, 2019.
The schools have met six times, the last in 1973. Ohio State holds a 4-1-1 series edge, with all games having been played in Columbus.
Ohio State athletic director Gene Smith said last week the Buckeyes plan to beef up their nonconference schedules in the coming years.
"Competing against programs from the state of Texas has always offered exciting experiences for our players and fans," Smith said in a statement Tuesday."TCU continues to be one of the top football programs in the country."
Ohio State president Gordon Gee didn't feel that way two years ago. He angered TCU supporters that fall when he said that neither the Horned Frogs nor Boise State -- who were both undefeated at the time -- deserved to play for the BCS national championship.
"Well, I don't know enough about the X's and O's of college football," Gee said at the time. "I do know, having been both a Southeastern Conference president and a Big Ten president, that it's like murderer's row every week for these schools. We do not play the Little Sisters of the Poor. We play very fine schools on any given day.
"So I think until a university runs through that gauntlet that there's some reason to believe that they not be the best teams to [be] in the big ballgame."