Thornton, 37, spent last season split between the Chicago White Sox and Boston Red Sox.
The veteran left hander finished 2013 with a 3.74 ERA and a 1.43 WHIP but held left handed batters to a .235 batting average. He will earn $7 million over the course of the two-year deal with the Yankees.
Yankees have signed lefty reliever Matt Thornton to a 2-year deal. He will make $3.5 million each season.
— Jack Curry (@JackCurryYES) December 17, 2013
Thornton will take over for another former White Sox left hander in Boone Logan. The Rockies signed Logan to a three-year deal worth $16.5 million.
If nothing else Thornton should offer the White Sox a capable left handed relief arm. Earlier on Monday the Yankees came to terms on a contract with second baseman Brian Roberts, formerly of the Baltimore Orioles.