He agreed to an eight-year deal with the Buckeyes and will receive $3 million per season, sources confirmed to ESPN on Friday.
"Chris is focused on academics, is a high-integrity person, a relentless recruiter with Midwestern ties and a proven winner," Ohio State athletic director Gene Smith said in a statement.
Holtmann, 45, will be formally introduced as the replacement for Thad Matta at a news conference Monday.
Holtmann was at Butler for four seasons, the last three as head coach during which he had a 70-31 mark. The Bulldogs reached the NCAA tournament in each of his three seasons in charge, winning 25 games and advancing to the Sweet 16 last season.
"Chris is a tremendous basketball coach, but more importantly, he is a great man who has led our program well and embodied The Butler Way during his time with us," Butler athletic director Barry Collier said in a statement.
Holtmann also spent three seasons as the coach at Gardner-Webb before leaving to become an assistant under Brandon Miller at Butler. He was named the Bulldogs' interim head coach in October 2014 after Miller took a medical leave of absence. The interim tag was removed in January 2015.
Ohio State parted ways earlier this week with Matta, who had three years remaining on his contract. The Buckeyes have missed the NCAA tournament in two straight seasons and struggled to a 17-15 record last season.
Smith said recruiting had fallen behind under Matta, who was not getting the best players in Ohio. All five of the players who made up Matta's 2015 recruiting class have transferred out of the program. Most recently, star guard JaQuan Lyle quit the team without publcly saying why, and starting center Trevor Thompson left early for the NBA.
ESPN's Jeff Borzello and The Associated Press contributed to this report.