A shooting guard, Tucker attended the University of Minnesota from 1978 to 1982, leading them to a Big Ten Conference championship in his senior year. He was then selected by the New York Knicks with the 6th overall pick of the 1982 NBA draft. One of the earliest three-point specialists, Tucker represented the Knicks in the first ever Three-point Shootout (1986), making it to the semifinals before being outpaced by Craig Hodges and eventual winner Larry Bird. Tucker would play nine seasons with the Knicks before joining the San Antonio Spurs in 1991, and after one season with the Spurs he joined the Chicago Bulls, who won the 1993 NBA Championship. He retired after that season, having tallied 6,237 career points and 1,532 career assists.