The schools announced the home-and-home series on Wednesday. The first game would be in Ann Arbor, Michigan.
The series matches two of the winningest program in NCAA history. Michigan ranks first with 912 victories, while Texas is third with 876.
Texas won the 2005 Rose Bowl 38-37 on a field goal on the final play of the Longhorns' first appearance in a Bowl Championship Series game. Quarterback Vince Young, who accounted for 372 total yards and five touchdowns against the Wolverines, led Texas to the national championship the next season.