The contract is reportedly worth a base salary of $1.25 million and will include another $1.4 million in performance bonuses.
MLB Network and FOX Sports' Ken Rosenthal, who first reported that the sides were nearing a deal, reported that Damon's contract would include a full no-trade clause, as well as an out clause that will allow the outfielder to seek free agency on a specified date following center fielder Grady Sizemore's return from the disabled list.
Damon -- a Scott Boras client -- acknowledged the deal in an interview with Jim Bowden and Casey Stern on the MLB Network Radio channel on SiriusXM.
"I had a conversation with them today," Damon said on Thursday. "I told them I've been staying in great shape, been running, been throwing, been hitting, been playing soccer. So I told them I feel like I could be ready in a couple of days. But I understand the grind of standing between innings and all that stuff, so I think I'm going to go out and work out for a week, and hopefully that's enough.
"Like I said, I've kept myself in pretty good shape, and I'm just excited that Cleveland is giving me this opportunity to see what I can do and also go help out a young team and provide some leadership to them."
Sizemore underwent surgery on his lower back on March 1 and is on the 60-day disabled list while he works through a rehab program in Cleveland. Sizemore is not eligible to be activated from the disabled list until June 3, and the Indians remain hopeful that the center fielder will be able to rejoin the team by then, or shortly after.
With Sizemore on the sidelines, the Indians have been using an outfield alignment of Shelley Duncan in left field, Michael Brantley in center and Shin-Soo Choo in right. Brantley moved from left to center following Sizemore's latest injury -- Sizemore has undergone six surgeries in the past four years for various issues -- and could move back to left upon Sizemore's return.
"Obviously, when Sizemore does come back, there's roster moves that have to happen," Damon said in the radio interview. "I'm going to do everything I can to play great, and hopefully when Sizemore comes back, there's still a spot for me, still some playing time for me. I know what Cleveland really wanted. They wanted somebody with a winning mentality and someone who has been there and done that, and obviously I've been around for a long time."
For the past two years, Cleveland used Duncan primarily as a right-handed option off the bench, adding depth to first base, designated hitter and left field. The Indians like Duncan in that reserve role, but gave him a chance to be the starting left fielder on Opening Day. With Damon in the fold, Duncan could move back to his bench role or platoon with the left-handed-hitting veteran.
Damon noted that the Indians have indeed offered him a role in left field.
"That's what Cleveland has offered me," he said. "I need to go out there and show people I can still play there. Right now, Shelley Duncan is the starting left fielder. I know they are going to rotate me in and give him a breather but, you know, I also understand this game, too. If Shelley Duncan is on fire at the plate, he's going to play. And if I am, they are going to find a place for me.
"So I'm going to go there and rejoin a few former teammates -- Shelley Duncan, Derek Lowe, Casey Kotchman -- and go and try to have as much fun as we can and try to win some ballgames."
One thing that is clear right now is that Cleveland needs to improve offensively.
Entering Thursday, when the Indians had a scheduled off-day, they were hitting .176, which ranked last among baseball's 30 teams. Cleveland managed 20 runs in five games, leading to a 1-4 record in season-opening series against the Blue Jays and White Sox. Considering the first two games included 28 innings, it is fair to note that Cleveland is averaging just 3.3 runs per nine innings.
Damon, 38, is a veteran of 17 seasons in the big leagues spent with the Royals, A's, Red Sox, Yankees, Tigers and Rays. He has 2,723 career hits, 277 from 3,000.
Last year, Damon hit .261 with a .326 on-base percentage, 16 home runs, 29 doubles, 73 RBIs and 19 stolen bases in 150 games for Tampa Bay. He was a designated hitter in 133 of those games.
Damon hit .285 with a .363 on-base percentage and an average of 19 homers and 74 RBIs from 2006-09, when he benefited from the short right-field porch at the old and new Yankee Stadiums. Since leaving New York, Damon has hit .266 with a .340 OBP and an average of 12 homers and 62 RBIs over the past two years with Detroit and Tampa Bay.