Dombrowski said the Red Sox are getting Pearce and cash considerations from Toronto in exchange for minor league infielder Santiago Espinal.
Pearce, 35, has hit .291 with 4 home runs and 16 RBIs in 26 games for Toronto this season. He has a career average of .255 and 83 career home runs and 268 RBIs.
Boston manager Alex Cora said the Red Sox are adding a strong batter they can use against left-handed pitching.
"It's one more weapon that we have. We got better tonight," Cora said. "It's good to have him."
Pearce could join the Red Sox this weekend in New York when they face the division rival Yankees.