On April 26, 1952, the Boston Celtics selected Conley with the 90th pick of the NBA draft. Playing 39 games as a rookie in the 1952-53 NBA season, Conley averaged about 12 minutes a game for a Celtics team that went 45-26 in the regular season under Red Auerbach. Conley did not play in the Celtics' two playoff series that season, with the team losing 3-1 in the Eastern Division finals to the New York Knicks.
After a five-year hiatus to focus on baseball with the Milwaukee Braves, Conley returned to the Celtics for the 1958-59 season, again seeing limited usage at about 13 minutes a game for a team that swept the Minneapolis Lakers 4-0 in the NBA finals. Conley averaged 4.2 points and 5.4 rebounds during the regular season and 4.9 points and 6.8 boards in the playoffs. Conley would have his best year as a Celtic the following season, averaging nearly 19 minutes a game during the regular season to score 6.7 points while hauling in 8.3 rebounds on average over 71 games in the regular season. The Celtics repeated as NBA champions with a 4-3 finals win over the St. Louis Hawks, with Conley roughly duplicating his regular season averages during the playoffs.
Conley would play on one more championship Celtics team during the 1960-61 season, culminating in a 4-1 defeat of the Hawks. Conley skipped the following NBA season while pitching for the Red Sox, then joined the New York Knicks where he averaged 9.0 points and 6.7 rebounds in 70 games during the 1962-63 season, before his minutes dropped precipitously the following year which was his last in the NBA.