Overbay appeared in 103 games for the Pittsburgh Pirates in 2011, but was unconditionally released August 9. The 34-year-old Overbay hit .227 with eight homers and 37 RBI before his release.
The D-Backs also placed Xavier Nady on the 15-day disabled list with a fractured left hand and designated pitcher Juan Jaime for assignment.
Nady, who hit .248 with four homers and 35 RBI over 82 with Arizona this season, suffered the fracture after he was hit by a pitch in Friday's game against the New York Mets.
Jaime has been sidelined since the 2009 season after undergoing Tommy John surgery on his right elbow. He has yet to appear in a major league game.