Cantu got two hits, scored twice and made an error in the Marlins' 5-0 win at San Francisco. The trade was completed right after the game ended.
"I'm going," Cantu said.
Texas acquired pitcher Cliff Lee from the Seattle Mariners earlier this month.
Cantu hit .262 with 10 home runs and 54 RBI for Florida. The Rangers already have All-Star Michael Young at third base -- Cantu said in recent days he was prepared to switch back to his former spot at first base, a position of need for the Rangers.