Gleeson played all or parts of five seasons (1936; 1939–42) in Major League Baseball for the Cleveland Indians, Chicago Cubs and Cincinnati Reds. In his best season, for the 1940 Cubs, Gleeson appeared in 129 games, batted 485 times and made 152 hits, including 39 doubles, 11 triples, five home runs and 61 runs batted in; he batted .313 that season. Overall, Gleeson appeared in 392 Major-League games, batting .263 with 16 home runs and 154 RBI. Defensively, he posted a .972 fielding percentage playing at all three outfield positions.
He remained in the game after his playing career ended as a minor leaguemanager, and Major League scout and coach. Although he worked for a time for his "hometown" Kansas City Athletics as a scout and Major League coach (1957), he spent much of his career in the New York Yankees' organization, serving as the first-base coach on Yogi Berra's staff during the Yanks' 1964pennant-winning season.
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