A baseball source told ESPN.com that Murphy is traveling to Fort Myers, Fla., for a physical exam and the deal was expected to be official later Monday.
Murphy, 34, will receive a base salary of $2 million if he makes Boston' s major league roster, according to ESPN.
The Red Sox drafted Murphy with the 17th overall pick in the 2003 draft.
Murphy hit .283 with 10 home runs and 50 RBIs in 132 games with the Indians and Angels last season. He has 104 career homers and 472 RBIs.