Overbay, who recently turned 36, has struggled the past couple of years, but he hit 20 homers in 2010 for Arizona. He ended last season with the Braves after being released by the Diamondbacks in August.
Overbay has a career .303 average against the Red Sox with 13 homers and 58 RBIs and an .888 OPS. At Fenway, he's hit .323 with four homers and 31 RBIs in 177 plate appearances, with an .895 OPS.
Overbay is considered a decent first baseman, and he'll likely start against the tough righthanded pitchers the Sox don't want Napoli to face. He could also be a late-inning defensive replacement.
The Red Sox had been looking for a lefthanded-hitting first baseman/outfielder but instead signed both Ryan Sweeney and Overbay to minor league deals. Both have a good chance of making the team.