The 27-year-old Frandsen, who has played second base, shortstop, third base and in the outfield, is expected to provide infield depth for the Red Sox.
"I think it gives us some depth that you don't know you'll need, but it would be a hard way to find out," said Red Sox manager Terry Francona, who described Frandsen as a "utility infielder type."
Frandsen played in 27 games for the Giants last season, batting .140. The season before, at Triple-A Fresno, Frandsen hit .295 with 13 homers and 55 RBIs in 110 games.
He is expected to report to Red Sox camp on Saturday.