After graduating from Corvallis High School, in Corvallis, Oregon, Gambee attended college at Oregon State University, where he played college ball for the Oregon State Beavers. He played four seasons at Oregon State, and averaged 18.8 points per game.
Gambee was selected in the first round (6th pick overall) of the 1958 NBA Draft by the St. Louis Hawks. After playing two seasons for the Hawks, he played three seasons with the Syracuse Nationals. After playing with the Nationals, he played four seasons for the Philadelphia Warriors. In his next season, he played with the San Diego Rockets. The next season he split between the Milwaukee Bucks and the Detroit Pistons. He played 59 games that season. In his final NBA season, Gambee played with the San Francisco Warriors. He scored a total of 7,935 points in his NBA career, grabbing 3,891 rebounds, making 757 assists, and playing 14,665 minutes.