The former Duke star lasted six seasons at the Big Ten school after four seasons at Seton Hall.
His overall record at Ann Arbor was 108-83, including a mark of 43-53 in Big Ten games. He had three 20-win seasons, but his teams never qualified for the NCAA Tournament.
"This is the toughest decision I've had to make since I've been athletic director," Bill Martin told the Detroit Free Press. "Tommy is a great guy. He provided leadership and helped moved the program forward from a difficult time. I'll never forget that. But this is in the long-term best interest of the program to change."
The newspaper said Amaker will receive a $900,000 payment under terms of his contract. His wife, Stephanie Pinder-Amaker, is Michigan's associate dean of students.