Batting lead off, Boston went 3-for-5 with a triple, stolen base, two RBIs and two runs scored in his major league debut on May 13.

Boston was given the opportunity to win the White Sox starting centerfield job for the 1985 season, although he struggled batting only .215 with three home runs and eleven RBIs when he was sent back down to triple-A.

[3] On July 23, the Sox traded left fielder Bobby Bonilla to the Pittsburgh Pirates for pitcher José DeLeón.

Cangelosi was shifted to left, and Boston, who was batting .303 in 96 games in Buffalo, was called back up to Chicago to take over in center.

He had his most productive season with the White Sox in 1987, when he batted .258 with ten home runs and 29 RBIs backing up Ken Williams and Gary Redus in center and left, respectively.

During the off season, the Mets signed free agent Vince Coleman to play center[7] with Boston taking on more of a fourth outfielder role.

Boston, Coleman and Dwight Gooden were accused of rape by Cindy Powell, who was also a known associate of a fourth teammate, David Cone.

Charges were dropped when Florida State Attorney Bruce Colton cited a lack of corroborating evidence and the nearly year long delay in Powell's complaint as reasons for the unlikelihood of conviction.

In 2013, then White Sox manager Robin Ventura named Boston the team's first base coach, a position he retained through the 2023 season.