Leach was a star quarterback at the University of Michigan from 1975 to 1978 under coach Bo Schembechler. He was the first NCAA Division I FBS player to pass for 200 points and score 200 points. He continues to hold the NCAA record for highest percentage of passes for touchdowns (400-499 attempts) with 45 in 462. A left-hander, he was given the starting job before his freshman year and held it until he graduated four years later. In his freshman year, with the Big Ten championship and a berth to the 1976 Rose Bowl on the line in the Michigan-Ohio State game, Leach threw an interception that was run back to the Michigan 3-yard line by Bruce West and set up the winning touchdown in a 21-14 Buckeye victory. However, Leach and the Wolverines never lost to Ohio State again in his career. One of the finest athletes in Michigan history, Leach was named All-Big Ten as a quarterback three times and also placed in the voting for the Heisman Trophy three times. He was co-MVP of the 1979 Rose Bowl, his last game as a Wolverine.
Leach shattered all Michigan's career passing, total offense and touchdown records. He set an NCAA record for most touchdowns accounted for (82) and broke Big Ten records for total offense (6,460 yards), total plays (1,034), and touchdown passes (48). In 1978, he finished third in balloting for the Heisman Trophy, behind Billy Sims and Chuck Fusina.
A standout on the diamond as well as the gridiron, Leach won the Big Ten batting championship as a junior and won the rare honor of being named All-American in both football and baseball.
He was selected in the first round by the Detroit Tigers in the 1979 amateur draft. He was also drafted by the NFL's Denver Broncos in 1979, but opted for a career in baseball. In a 10-year career, he played for the Tigers, Toronto Blue Jays, Texas Rangers and San Francisco Giants, mainly as a part-time outfielder and DH. His best season came in 1986, when he hit .309 in 110 games. In 1990, he was suspended for 120 days by Major League Baseball Commissioner Fay Vincent for a positive drug test and underwent league-ordered drug treatment.
In October 2009, Leach criticized former Michigan head football Lloyd Carr for mingling with University of Iowa athletic personnel during Michigan's 30-28 loss at Iowa. During a phone call to Ann Arbor sports talk radio station WTKA, Leach said "Our ex-coach flipped a huge middle finger right in our current coach's face". Ask people to investigate that, there will be a lot more there". Leach's comments fueled debate concerning division within the Michigan football community over the hiring of Rich Rodriguez as head football coach.