Abbott was born in Flint, Michigan. He was picked up by the Ypsilanti, Michigan, American Legion team and went on to win the championship. He graduated from Flint Central High School in Michigan where he was a stand-out pitcher and quarterback. He played for the Grossi Baseball Club during the summer in the Connie Mack leagues of Michigan. He was drafted in the 36th round by the Toronto Blue Jays in the 1985 Major League Baseball draft but did not sign, instead moving on to the University of Michigan.

He played for Michigan three years under coach Bud Middaugh, from 1985 to 1988, leading them to two Big Ten championships. In 1987, he won the James E. Sullivan Award as the top amateur athlete in the United States, becoming the first baseball player to win the award. Abbott was the flag-bearer for the United States at the 1987 Pan American Games in Indianapolis, helping lead the US to a second-place finish. Baseball was a demonstration sport in the 1988 Summer Olympics; Abbott pitched the final game, winning an unofficial gold medal for the United States. Abbott was voted the Big Ten Athlete of the Year in 1988. He would be selected 8th overall by the California Angels in the 1988 draft. Abbott’s University of Michigan #31 jersey was retired at the Wolverines’ April 18, 2009 home game against Michigan State University.

In 1989, Abbott joined the California Angels’ starting rotation as a rookie without playing a single minor league game. That season, he posted a 12-12 win–loss record with an earned run average (ERA) of 3.92, and finished fifth in the year’s American League (AL) Rookie of the Year Award voting.

In 1991, Abbott went 18–11 for the Angels, who finished in last place in the AL West with an 81–81 record. Abbott posted the fourth-lowest ERA in the AL (2.89) while pitching 243 innings. As a result, Abbott finished third in the AL Cy Young Award voting. In the 1992 season, he posted a 2.77 ERA (fifth-lowest in the AL) but his win–loss record fell to 7–15 for the sixth-place Angels. Abbott also won the Tony Conigliaro Award in 1992.

Batting was not an issue for Abbott for the majority of his career, since the American League uses the designated hitter, and he played only two seasons in the interleague play era. But Abbott tripled in a spring training game in 1991 off Rick Reuschel, and when Abbott joined the National League’s Milwaukee Brewers in 1999, he had two hits in 21 at-bats, both off Jon Lieber. New York Yankees teammate Mariano Rivera claimed to have witnessed Abbott hitting home runs during batting practice.

In the offseason, the Angels attempted to trim payroll and traded Abbott to the New York Yankees for their top minor league prospect first baseman J.T. Snow, pitchers Russ Springer and Jerry Nielsen. Abbott had an up and down year for the Yankees but on September 4, 1993, Abbott pitched a no-hitter against the Cleveland Indians. On November 26 in the same year, Abbott appeared as himself on the TV series Boy Meets World in the episode “Class Pre-Union”.

In 1994, Abbott’s Yankees led the AL East, but the season halted, and the playoffs were canceled, due to a players strike on August 12. The following year, after starting the season with the Chicago White Sox, he returned to the Angels, who held an 11-game lead over the Seattle Mariners in August, but lost the AL West division title in a one-game playoff to the Mariners.

Abbott returned to the White Sox in 1998, starting five games and winning all five. Abbott continued his comeback the following year with the Milwaukee Brewers, but pitched ineffectively. This was the first time he had played for a National League team, forcing him to bat for the first time in his career. He recorded two hits in 21 at bats during his Brewers stint. Both of his hits scored runs, and both of hits came off of Chicago Cubs pitcher Jon Lieber, albeit in different games.

In 2007, Abbott was elected to the College Baseball Hall of Fame for his career at Michigan.

In April 2012, Abbott’s autobiography, Imperfect: An Improbable Life ( ISBN 0345523253), co-written with Tim Brown, was published by Ballantine Books.