Tuck, 58 and an Indiana resident, would've entered his seventh season as the Sox's bullpen coach. Boston's Minor League catching coordinator, Chad Epperson, could be a candidate to fill Tuck's job.
Tuck has coached or scouted for seven teams that have reached the World Series, with five of those clubs winning titles. He spent a long time with the Yankees before joining the Sox, and has also worked with the Astros, Indians and Marlins.
WEEI.com first reported on Tuesday that Tuck would not return for the 2013 season.
Evan Drellich is a reporter for MLB.com. Follow him on Twitter @EvanDrellich. This story was not subject to the approval of Major League Baseball or its clubs.