The 6-foot-5, 195-pound senior-to-be is the No. 9 pro-style quarterback in the country according to 247Sports Composite rankings. He's the No. 6 prospect in Michigan and No. 251 overall nationally.
Mathis had numerous other offers, including from Oregon, Pitt, South Carolina, Kentucky, Cincinnati and Iowa State.
His commitment came after Ohio State unsuccessfully pursued several quarterbacks, including Texas four-star Grant Gunnell (who committed to Arizona) and Kansas four-star Graham Mertz (Wisconsin).
Alter's Connor Bazelak, the top-rated QB prospect in Ohio, threw for Buckeye assistant coaches on two occasions but did not receive an OSU offer before committing to Missouri last week.
Ohio State's 2019 class is ranked ninth in the country, one spot ahead of Michigan.
The Wolverines had a big weekend, adding commitments from four players including Fairfield tight end Erick All.
READ MORE: 7 thoughts on Ohio State-Michigan and beyond | Charles Woodson is probably wrong about The Game