Harris spent most of his playing career as a second baseman with the Washington Senators (1919–28). In 1924, he was named player-manager of the Senators; at the age of 27 he was the youngest manager in the majors. He led the Senators to their only World Series title in Washington in his rookie season. He won a second consecutive American League pennant in 1925, but the Senators lost the 1925 World Series in Pittsburgh in the late innings of Game 7 after leading 3-1 in the Series. Baseball historian William C. Kashatus wrote of his dominant play in the 1924 World Series: "Not only did he set records for chances accepted, double plays and put-outs in the exciting seven-game affair, but he batted .333 and hit two home runs".
His initial departure from the Senators in 1928 (he would twice return to manage them again from 1935 to 1942 and 1950 to 1954) came as a trade to the Detroit Tigers as player-manager. However, for all intents and purposes, 1928 was his last year as a full-time player. He only made 11 cameo appearances in the Tigers lineup—seven in 1929 and four in 1931. He managed the Tigers twice (1929–33, 1955–56), Boston Red Sox (1934), Philadelphia Phillies (briefly known as the Blue Jays, 1943) and the 1947 World ChampionNew York Yankees, staying on in 1948, when they finished a close third to Cleveland and Boston. He closed his 29-year managing career with the 1956 Tigers, rejoined the Red Sox as assistant general manager in 1957–58 and succeeded Joe Cronin as Boston's GM in January 1959, serving two seasons in that post before being let go in September 1960. On his watch, the Bosox finally broke their own baseball color line by promoting Pumpsie Green from Triple-A on July 21, 1959, the next-to-last MLB team to do so except for the Tigers (in 1961), more than twelve years after Jackie Robinson's debut with the Brooklyn Dodgers. He ended his long MLB career as a scout for the Chicago White Sox and special assistant for the new expansion Washington Senators franchise that played in D.C. from 1961 to 1971 before moving on to Arlington, Texas.