The Indians will likely make an official announcement on Monday.
The left-handed-hitting Murphy would project to be the primary right fielder for the Indians, who used Drew Stubbs in the starting role last season. Stubbs' offensive struggles, especially against right-handed pitching, combined with the fact that he is eligible for arbitration, make him a candidate to either be traded or non-tendered.
Should Cleveland choose to keep Stubbs in the fold, he could serve as a fourth outfielder, taking starts in right field against left-handed pitchers. Ryan Raburn, who filled that type of backup role last season, is also under contract for 2014 for the Indians. Left and center field are currently occupied by Michael Brantley and Michael Bourn, respectively.
The 32-year-old Murphy has spent parts of eight season in the Major Leagues between stints with the Red Sox and Rangers. He suited up for the Red Sox in the 2006 and '07 seasons, when Indians manager Terry Francona was the manager in Boston.
Last season, Murphy posted a .220/.282/.374 slash line with 13 home runs, 26 doubles and 45 RBIs in 142 games (476 plate appearances) for Texas, which used him as a part-time outfielder and pinch-hitter as the season progressed. It was a disappointing dropoff from Murphy's showing in 2012, when he hit .304 with 15 homers, 61 RBIs and an .859 OPS for the Rangers.
Murphy, who earned $5.775 million last season, has spent the majority of his career in left field, but he has experience at all three outfield spots. Over the course of his eight seasons, he has also posted a .280 average and an .816 OPS against left-handed pitchers, compared to a .249 average and .657 OPS against righties.
Interestingly, the signing was initially reported by Texas sportswriter Jamie Kelly, who was told by one of her followers on Twitter that Murphy's daughter was spreading the word at daycare. When Murphy arrived to pick her up, he confirmed the news to the teachers.
Stubbs -- acquired from the Reds in a three-team, nine-player trade last winter -- moved from center field to right for the Indians and hit .233 with 10 homers, 45 RBIs and a .665 OPS in 146 games. Stubbs hit just .216 (.637 OPS) against right-handed pitching on the season and slumped to a .192 average (.572 OPS) in September.
Through arbitration, the 29-year-old Stubbs earned $2.825 million last season and would be scheduled for a raise this offseason.
Raburn, who signed a two-year extension with the Indians in August, hit .272 with 16 home runs, 55 RBIs and a .902 OPS in 87 games as a role player last season. The right-handed-hitting utility man made 46 starts in right field and ended the season batting .308 with a 1.020 OPS against left-handed pitchers.