Cooper was selected by the Boston Red Sox in the 1968 draft and made his Major League debut with the Red Sox in 1972. Before the 1977 season, he was sent to the Milwaukee Brewers in the same trade that brought George Scott back to Boston.
In 1983 Cooper hit .307 with 30 home runs and a league-leading and career-high 126 RBIs. He also posted three seasons with 200-plus hits, in 1980, 1982 and 1983, finished fifth in the AL MVP vote, and was named the Brewers' team MVP in three seasons (1980, 1982–83). An excellent defensive first baseman, he was a two-time Gold Glove winner (1979–80). He also won the Silver Slugger Award in three straight years (1980–82); the only other Brewer to have done so is Ryan Braun (2008–10).
Cooper concluded his Major League career with 11 seasons as a Brewer, including an appearance in the 1982 World Series. Cooper holds the Milwaukee franchise records for hits (219 in 1980). Cooper held the team record for RBIs in a season with 126 until Prince Fielder broke that record on September 19, 2009 against the Houston Astros, who Cooper was managing at the time. Through 2011 he was one of three Brewers who have had four 100-RBI seasons, along with Prince Fielder and Ryan Braun.
In 1983 he was honored with the Roberto Clemente Award, and in 2002 he was inducted into the Brewers Walk of Fame.
Following the conclusion of his playing career, he worked in several capacities in the Brewers organization. He was named bench coach for Milwaukee in 2002 and also managed the Triple-A Indianapolis Indians in 2003–04. He returned to the Major League coaching ranks in 2005 as a bench coach for the Houston Astros.
On August 27, 2007, he was named the interim manager of the Astros following the firing of Phil Garner, making him the first African American field manager in Astros' history. Cooper's previous managerial experience was at Class AAA Indianapolis, the Milwaukee Brewers' top farm club. Cooper had a record of 130–156, finishing fourth in 2003 and third in 2004. On September 28, 2007, Cooper's interim tag was dropped and he became the Astros' 16th manager. Cooper was released as Astros manager on September 21, 2009.