Well known for his defensive abilities, Cooke was a competent fourth outfielder able to handle all three outfield positions. He reached the majors in 1930 with the New York Yankees, spending three years with them before moving to the Boston Red Sox (1933-1936) and Cincinnati Reds (1938). His most productive season came in 1933 with Boston, when he hit .293 and posted career-numbers in games played (119), runs (86), doubles (35), triples (10), and runs batted in (54). In 1935 he batted a career-high .306 in 100 games while compiling a .400 on-base percentage (10th in the American League).
In an eight-season career, Cooke was a .280 hitter (489-for-1745) with 24 home runs and 229 RBI in 608 games, including 324 runs, 109 doubles, 28 triples, 32 stolen bases, a .384 on-base percentage, and a solid walk-to-strikeout ratio of 1.06 (290-to-276).
Following his playing career, Cooke joined the Navy in 1942 and served in Okinawa during World War II. While at the Navy, he received training in fitness conditioning. After discharge, he became the trainer for the Philadelphia Phillies in 1946. He later coached for them from 1948 to 1952, serving also as an interim manager during the 1948 midseason while posting a 6-6 record (.500).
Cooke died in Raleigh, North Carolina at age 80.