Cooper turned professional in 1938. In the ten-year span between 1949 and 1958, he won five official PGA Tour events and had runner-up finishes in the 1950 Houston Open and the 1955 Tournament of Champions. His best finish in a major was T-4 at the 1953 U.S. Open. He helped a young Chi Chi Rodriguez improve enough to secure a spot on the PGA Tour.
Cooper won the 1976 Senior PGA Championship at the age of 61 with a four-day total of 283 over runner-up Fred Wampler. The tournament was held at Walt Disney World in Orlando, Florida.
Cooper lived in Lakeland, Florida, where he owned the Par 3 and Lone Palm Golf Club. He was also active in golf course design.