Wolf is 132-117 with a 4.20 ERA in 376 games in parts of 14 major league seasons. The 37-year-old Wolf underwent reconstructive elbow surgery and missed all of last season. He pitched for Baltimore and Milwaukee in 2012.
Wolf was in the spring training camp of the Seattle Mariners this year but failed to make the major league roster.
He will report to Triple-A Reno but could be with the big club if he shows any effectiveness, given the struggles of the Diamondbacks' rotation.
Arizona announced the deal on Friday.