Valverde, who saved 110 games for Detroit from 2010-12, wasn't invited back after surrendering nine runs and 11 hits in four post-season appearances last year.
Detroit signed the 35-year-old to a minor-league deal April 4. The hurler logged three scoreless relief outings for Class A Lakeland, earning him a deal worth at least $2 million, Fox Sports reported.
The Tigers made the move after a "bullpen-by-committee" experiment by Manager Jim Leyland produced mixed results in the first month of the season.
Valverde, nicknamed "Papa Grande" and known for his colorful antics on the mound, has compiled 277 career saves over 10 seasons with Arizona, Houston and Detroit.
The Tigers designated pitcher Duane Below for assignment.