Thornton, 37, appeared in 60 games last season between the White Sox and Red Sox, posting an 0-4 record and a 3.74 ERA. He struck out 30, walked 15 and gave up 47 hits in that span, holding lefties to a .235 (19-for-81) average and a .638 OPS.
Thornton was traded from Chicago to Boston on July 12, and he made his last 20 appearances with the Red Sox. He did not pitch in the postseason.
Thornton is the only Major Leaguer to make at least 55 appearances in each of the last nine seasons and the first to have eight straight years of at least 60 games pitched since Mariano Rivera and Francisco Cordero accomplished the feat from 2003-11. He is the White Sox's all-time leader with 512 relief appearances.
The Yanks designated outfielder Vernon Wells for assignment on Friday morning to make room on the 40-man roster.
Joey Nowak is a reporter for MLB.com. Follow him on Twitter at @joeynowak. This story was not subject to the approval of Major League Baseball or its clubs.