WBZ-TV in Boston reported Damon's departure for Boston's arch-rival just before 11 p.m. ET. The deal, which was confirmed by a Yankees official, is contingent on Damon passing a physical.
"They were coming after me aggressively," Damon told the station in an exclusive interview. "We know George Steinbrenner's reputation. He always wants to have the best players and I think he showed that tonight. He and [general manager] Brian Cashman came after me hard, and now I'm part of the Yankees and that great lineup. We're going to be a tough team to beat."
Before Tuesday night's stunning development, the Red Sox had made the only formal proposal, a four-year, $40 million package at the Winter Meetings in Dallas. Damon said the Red Sox did not try to match it and that he personally had only spoken with manager Terry Francona shortly after the season ended.
"I made contact with them and told [Francona] they really need to get going because if not, I'm going to be on another team," Damon said. "Unfortunately, Boston had their plans. I'm not sure if they knew I meant it, but now I'm a Yankee, and hopefully they can go off and get the other center fielders they've been courting for the past month or so."
The club had been considering options for replacing Damon, including trading for Cleveland's Coco Crisp or Seattle's Jeremy Reed.
"More teams have traded for or signed center fielders so I think the market, in some ways, is clearer," co-Red Sox GM Jed Hoyer said earlier in the day during a conference call to discuss off-season moves. "There are more knowns now than unknowns. Our absolute priority is to bring Johnny back and have him in center field next year, but we'd be irresponsible if we just sat back and didn't explore other alternatives."
Considered one of the best leadoff hitters in the game, Damon adds yet another weapon to an already potent Yankees lineup.
"They haven't had a championship since Chuck Knoblauch was there, when they had a great leadoff hitter," Damon said. "I think the leadoff role has been underappreciated. A good leadoff hitter is tough to find and I think New York just found the best leadoff hitter in the game."
Damon told the station he will miss the Fenway faithful, who transformed him from an All-Star outfielder to a national cult hero, making it cool to be an "Idiot."
"My message to Red Sox fans is I tried, I tried everything in my power to come back, but unfortunately, I know they're going to be upset," he said. "I'm always going to have a strong feeling about them and I'm always going to remember the great times and the World Series and [how] three out [of my] four years there, we made the playoffs.
"I just want them to know that I appreciate them and I tried and that's the least I can do. I know they're going to continue to root for the Red Sox, which they should, and I'm going to win another World Series, so that's going to have to be right now. It's going to be tough to say bye to some of the greatest fans in the world. Unfortunately, they had to see this day and it's time to move forward."
Damon said he'll have no problem cutting the most famous hair in baseball to conform to New York's grooming code.
"Without a doubt, George Steinbrenner has a policy and I'm going to stick to it," he said. "Our policy with the Yankees is to go out there and win and we're going to try and bring another championship to them."
The wheels for Tuesday's dramatic decision were set in motion when Damon did the expected Monday and rejected arbitration.
Damon's tenure in Boston began before the 2002 season, when then-GM Dan Duquette signed him to a four-year, $32 million contract, and his tenure was highlighted by his 2004 campaign. He batted .304 with 20 homers and 94 RBIs in helping the Red Sox win their first World Series in 86 years.
Mike Petraglia is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.