Wagner started 27 games last season, averaging 11.6 points and leading the team in steals. The 6-foot-9 German missed the first four games because of a fractured wrist.
"Returning to Michigan is the right step for me not only as a basketball player, but as a person, too," Wagner said in a statement Thursday. "This first season was a transition, competitive, fun and one of growth. I am very much looking forward to getting back to Ann Arbor and living that again."
Wagner, the brother of former Michigan star Moe Wagner, shot 31% from beyond the arc in 2019-20 and was second on the team in 3-point attempts.
"Franz and I have had many wonderful conversations since the end of the season. He really took the opportunity to look into everything he could before making his final decision -- a decision we are elated for," Michigan coach Juwan Howard said. "His leadership, work ethic and desire to make not only himself, but his teammates better is incredible."
Michigan also announced that forward Austin Davis had surgery Monday on his right shoulder and is expected to recover fully. He could be ready to return in early October.