The minor league deal includes an invitation to spring training.
Branyan, 36, has played for 11 teams since appearing in his first major league game for Cleveland in 1998.
He appeared in 68 games for the Diamondbacks and Angels last season and is a career .232 hitter with 194 homers and 467 runs batted in.
In its story, MLB.com noted that Branyan has two of the longest home runs hit at the new Yankee Stadium. He hit the only homer into the upper deck of the stadium in 2010.