It's a minor league pact, so the 38-year-old Damon will spend two weeks in the minors before being added to the 40-man roster in early May.
The only problem is that we don't know how much Damon will be playing.
He's played just 44 games in the outfield the past two seasons, but he's played 230 games at designated hitter.
Travis Hafner is entrenched at DH, while the outfield is currently comprised of Shelley Duncan, Michael Brantley and Shin-Soo Choo.
Manny Acta will have some shuffling to do, but it's likely that Damon will get his fair share of at-bats.
Here are my predictions for Damon's season.
Acta will have no choice but to put Damon in the starting lineup this season, as his veteran experience and solid bat will greatly benefit the team.
Last season, Damon played in 150 games for the Rays. He hit .261 with 16 home runs and 73 RBI.
He recorded 152 hits, 29 of which were doubles.
It's not yet known as to how well he'll produce this season, especially considering the fact that he'll be starting the season late.
Given 10-15 games to get back into shape this season, he'll earn his spot in the lineup.
He still may sit against lefties on occasion, but he'll probably replace Duncan in left field come the end of May.
Damon recorded more than a hit per game last season, but it's unlikely that he'll be able to do the same in 2012.
He's just 277 hits away from 3,000 for his career, so he might even press a bit to get there.
It obviously won't happen this season, but he's still close enough to start worrying about it.
That many hits will probably equate to a .260 average, which will be a nice upgrade over the inconsistencies of Duncan.
Out of the 100 or so hits, 20 will be doubles and three will be triples.
Despite Damon's age, bat speed is not his problem.
His bat speed and natural uppercut has always helped him to hit home runs, and that won't change in 2012.
He's hit at least 15 home runs in three of the past four seasons, so there's little reason to believe that he won't be able to do it again.
He'll likely finish third or fourth on the team in home runs, as Carlos Santana, Hafner and Choo will approach 20 each.
Regardless of where he finishes on the team, his extra offense will be a nice addition to the Indians' lineup.
Damon had problems getting on base last season—his .326 OBP was the worst since 2001 as a member of the Athletics.
He'll likely bring that back up to a more respectable level, as he'll probably be hitting towards the top of the order.
That OBP will translate to a stolen base total of around 25 and a runs scored total of around 85.
Last season he stole 19 and scored 79, so we can definitely expect an increase in those categories.
The Indians really don't have another base-stealing threat on the roster, so Damon will be the primary option on the basepaths.
Even though he's played just 44 games in the field over the past two seasons, Damon still has the speed and range to be a serviceable outfielder.
He made just two errors while with the Tigers, and none last season in Tampa Bay.
He may not have the strongest arm anymore, but he releases the ball quick enough to make up for his lack of arm strength.
He'll probably start about 75 games in the outfield this season, so I'd expect about three errors.
Will he play Gold Glove-caliber defense? No.
Will he play well enough that the Indians won't regret putting him out there? Yes.