According to Paul Hoynes of the Cleveland Plain Dealer, the deal will pay Murphy $12 million over the next two seasons, and also includes a club option for 2016. The contract is pending a physical.
Murphy, 32, was not expected to return to the Rangers after hitting .220 with 13 HR and 45 RBI in 142 games last season.
The team has set their sights on more expensive outfield targets like Shin-Soo Choo and Nelson Cruz, meaning that Murphy had to look elsewhere to find work.
In eight seasons since being acquired from the Red Sox in a trade that sent Eric Gagne to Boston, Murphy has hit .275 with 85 HR and 362 RBI in seven seasons with Texas. He has appeared at all three outfield spots, and will join Michael Brantley, Michael Bourn, Drew Stubbs and Ryan Raburn in a crowded Indians outfield.
With Stubbs reportedly drawing trade interest from many teams, the Indians could trade him and slot Murphy into right field on a more-permanent basis with Raburn serving as their fourth outfielder. If the team is unable to find a suitable trade involving Stubbs, they could refuse to tender him a contract, which would make him a free agent.