The Yankees announced the deal Sunday.
The 31-year-old Young started this year with the New York Mets and was released in early August after a season-long slump. He made his debut with the Yankees in early September and homered in three straight games, then stole home in another game.
Young hit a combined .222 with 11 homers and 38 RBIs for the Yankees and Mets last season.
Young has also played with Arizona and Oakland during nine seasons in the majors. He is a career .234 hitter with 155 homers, 486 RBIs and 130 steals, and was an NL All-Star in 2010.