During his 14-year baseball career, Belcher pitched from 1987–2000 for seven different ballclubs: the Los Angeles Dodgers (1987–1991), Cincinnati Reds (1992–1993), Chicago White Sox (1993), Detroit Tigers (1994), Seattle Mariners (1995), Kansas City Royals (1996–1998), and Anaheim Angels (1999–2000).
Belcher played high school baseball at Highland High School and intercollegiate varsity baseball at Mount Vernon Nazarene College in Mount Vernon, Ohio. He was the first draft pick in the 1983 Major League Baseball Draft, selected by the Minnesota Twins. However, he refused to sign with the Twins, and instead was selected in the 1984 supplemental draft by the New York Yankees. He was picked up by the Oakland Athletics in the compensation pool.
After climbing through the A's system to Triple-A, he was traded to Los Angeles on September 3, 1987, as the "player to be named later" in the Rick Honeycutt transaction. He made his MLB debut on September 6 as a Dodger. Belcher was a member of the 1988 Dodgers team that won the World Series, defeating the Oakland Athletics. Belcher won one game in the World Series after winning twice in the National League Championship Series. The next year he led the National League with 10 complete games and MLB with eight shutouts – the most since Roger Clemens of the Boston Red Sox the previous year, while placing in the top ten in wins and ERA. He was the last starting pitcher in the majors to have more than five shutouts, until 2011, when Cliff Lee of the Philadelphia Phillies had six on the season.
However, his stay in Los Angeles proved brief, as he was traded to the Reds in 1991 as a part of the Eric Davis multi-player transaction. He tied a career high with 15 wins for the Reds, but was dealt again, this time to the White Sox in the middle of the 1993 season at the trading deadline. He won Game Four of the American League Championship Series in relief against the Toronto Blue Jays. Filing for free agency, he signed with the Tigers for 1994, but led the American League in losses with 15 that strike-shortened year.
He returned in 1995 to the Reds on a one-year minor-league contract, but was soon dealt by them a second time, this time in May to the Mariners. New York Yankees superstar shortstop Derek Jeter got his first major league hit off Belcher in the Kingdome on May 30, 1995. At the end of the regular season, Belcher lost two post-season games, the only two playoff losses he suffered in his career; after Game 2 of the 1995 American League Division Series, he assaulted a cameraman in the locker room area for filming him after giving up a game-winning home run to Yankee catcher Jim Leyritz. Again becoming a free agent, he signed with the Royals for the 1996 season, spending the next three years with Kansas City and leading the team in wins each season.
On June 5, 1999, Belcher was involved in an on-field brawl at Dodger Stadium. At the time a member of the Anaheim Angels, Belcher was involved in an altercation with then-Los Angeles Dodgers pitcher Chan Ho Park. Park claimed that Belcher had tagged him too hard on the just-concluded play and asked him about the incident. Belcher remarked with racist comments causing Park to kick him.
Belcher played his final game on September 30, 2000. He retired in spring training in 2001, his effectiveness gone following a series of injuries.
On November 6, 2009, Belcher was named pitching coach for the Cleveland Indians after spending the last eight seasons in the Indians organization as a Special Assistant to Baseball Operations. In 2012, he resumed this position with the Indians, which he currently holds as of June 2014.
Belcher resigned his position as pitching coach in September 2011.