Schembechler, who leaves coaching without having won a national championship, will remain as athletic director - a post added to his title in 1988 when Don Canham retired.
But Schembechler said he was uncertain how long he would stay on as athletic director because he said he was concerned that his name and presence might overshadow his successor.
"I'm not sure what I'm going to do. When I took that job, I felt I would coach for the next five years and at the end of that time, retire completely.
"I'm not sure that it's in the best interest of Michigan or the program or myself or Gary Moeller for me to be hanging around. It might be pretty difficult for me to sit in the athletic director's chair. I'd want to go to practice, and I don't think I should do that," Schembechler said.
Moeller, however, said he'd have no problems with Schembechler as athletic director.
"Bo kept saying, 'You don't want me around, you don't want me around, you don't want me around,' " Moeller said. "But I told him he wasn't going to bother me. I would welcome him at any time.
"I know he'll be here for the Notre Dame game next year - he's going to have to talk to the team. We're going to use him a lot. This is going to be Gary Moeller's program - but there will be a lot of Bo Schembechler in it."
Schembechler hinted that he was stepping down on Monday when he told a university sociology class that he would never sit in the coach's office of the new $12.5 million Center of Champions. The building, to be completed next fall, will house the football program.
Heart attacks in 1970 and 1987 resulted in open-heart surgery, and Schembechler's physicians have urged him to slow down ever since.
Apparently, the decision was made a little easier because No. 3 Michigan just won its second straight Big 10 title.
Schembechler said he decided to make the announcement now because he wanted prospective recruits to know that Moeller would be their coach.
Southern Cal coach Larry Smith, who will be on the opposite sideline on New Year's Day in Pasadena, said he was saddened by the news.
"It's a shock. All of a sudden, Bo is out of the game," he said. "Anyone who has coached with or played for Bo thought that he'd coach forever. College football is losing a great contributor."
Schembechler leads all coaches in NCAA Division I-A with a record of 234-64-8 after 21 years at Michigan and six at Miami of Ohio. He is fifth on the all-time list and needed only four more victories to match his mentor at Ohio State, Woody Hayes. Schembechler is the winningest coach in Michigan history at 194-47-5.
Schembechler never had a losing season. Fifteen of his 21 Michigan teams have been ranked in the top 10 nationally. The 1985 team finished No. 2 after beating Nebraska in the Fiesta Bowl.
The Wolverines began the 1989 season ranked No. 1, but lost their opening game to Notre Dame before getting 10 straight wins.
"If you think that my career has been a failure because I have never won a national title, you have another think coming," Schembechler said before beating Ohio State in the final regular-season game. "I have never played a game for the national title. Our goals always have been to win the Big 10 title and the Rose Bowl. If we do that, then we consider it a successful season."
This year's Rose Bowl will be Schembechler's 10th and third in the last four years.
Schembechler transformed Michigan's program into one of the best in the nation and began to regularly fill the university's 101,701-seat stadium. The Wolverines have played to 91 consecutive home crowds in excess of 100,000.
Schembechler also became a spokesman for college football, urging tight academic standards and higher graduation rates for players.
"He's meant a great deal to all of intercollegiate football," Purdue coach Fred Akers said. "He'll be missed. I can't think of anyone who deserves more of a well-earned rest."
Moeller, 48, has been an assistant to Schembechler for 18 years. He rejoined the Wolverines' staff in 1980 after three years as coach at Illinois, where he was released after compiling a 6-24-3 record.
Moeller led Michigan to a 28-24 victory over Alabama in the 1987 Hall of Fame Bowl while Schembechler was recovering from his second open-heart operation.