Sweeney, who could have filed for arbitration, made $1.4 million last year with the Oakland Athletics. He is expected to compete for playing time in right field, where the Red Sox have a vacancy after deciding not to retain free agent J.D. Drew and trading Josh Reddick to Oakland.
In six seasons, Sweeney has a .283 batting average after hitting .265 with one homer and 25 RBIs in 264 at-bats last season.
The Red Sox obtained him and closer Andrew Bailey on Dec. 28 for Reddick, infield prospect Miles Head and minor league pitcher Raul Alcantara.