The Wolverines will host the Longhorns in Ann Arbor, Mich. on Aug. 31, 2024, and Texas will face Michigan in Austin, Texas, on Sept. 4, 2027.
The UT System Board of Regents will consider the agreement in November.
"A match-up of this magnitude doesn't come along all that often, and when it does it's special for both programs and the great fans that support each institution," said Michigan coach Brady Hoke. "This also is a special series for all fans of college football, and I anticipate great games just like the first contest played between the two programs."
The lone previous game between the two schools came in the Rose Bowl following the 2004 season, with Texas winning 38-37.
Michigan is 2-1 this season, while Texas is 1-2.
- Chris Johnson