Volquez, a starter for most of his 14-year career, will be a reliever for the Rangers this season. He missed most of last season with an elbow injury but returned in September and pitched out of the bullpen for the Rangers.
"I was excited for him," Woodward told reporters, according to MLB.com. "He has done a really good job with the arm and how the ball is coming out of his hand. There are so many things about Volquez that we love. First and foremost, the stuff is there. I wasn't going to keep him unless he showed he can get people out."
Pitching this season marks a change of plans for Volquez, who had indicated last season that he had planned to retire.
Volquez was in the Rangers' summer camp on a minor league contract.