The Wolverines and Huskies will meet Sept. 5, 2020, in Seattle, and Sept. 18, 2021, in Ann Arbor, Michigan.
Michigan leads the all-time series with Washington 7-5, and the Wolverines won the teams' last contest in 2002.
Washington on Wednesday also announced a home-and-home series with BYU to be played in 2018 (home) and 2019 (road).
Michigan and Washington have met four times in the Rose Bowl, with each team winning twice. Michigan is 3-1 at Michigan Stadium and 2-2 at Husky Stadium.
"There have been some exciting, down-to-the-wire football games between Michigan and Washington, and we anticipate the same type of contests when this series is played at the outset of the next decade," Michigan coach Brady Hoke said in a prepared statement.
Michigan is diversifying its upcoming schedule with opponents like Oregon State, Florida, Colorado and Arkansas. The Wolverines will play Notre Dame for the final time in the foreseeable future Sept. 6 at Notre Dame Stadium.