The New York Post was the first to report that the Yankees had come to terms with Winn, 35, who batted .262 with 33 doubles, two home runs, 51 RBIs and 16 stolen bases in 149 games for the Giants last season.
The speedy switch-hitting veteran has compiled a career batting average of .286 across 12 Major League seasons with the Rays, Mariners and Giants, and the signing appears to complete what will be the Yankees' outfield arrangement for 2010.
Winn's contract will be worth approximately $2 million.
With negotiations having long since stalled with free-agent Johnny Damon, general manager Brian Cashman had outlined his priorities heading into the spring as adding one more right-handed bat to an outfield mix that includes Curtis Granderson, Nick Swisher and Brett Gardner.
Saying that they only had approximately $2 million to $3 million to fill its remaining needs, New York had shown levels of interest in both Rocco Baldelli and Reed Johnson, seeking someone who hits left-handed pitching well and could platoon with Gardner.
But though Winn struggled against left-handed pitching, batting just .158 against southpaws in 2009, he gives the Yankees a player who is capable of playing all three outfield positions and adds a high-percentage stolen-base rate to the bottom half of the lineup. He could share time with Gardner in left field or perhaps win the job outright in the spring.
The Post also reported that the Yankees could be closing in on a Minor League contract with Baldelli, which would pit him against such roster hopefuls as Rule 5 Draft selection Jamie Hoffmann and speedster Greg Golson, who was acquired from the Rangers on Tuesday for a Minor Leaguer.
Cashman said on Tuesday that the need for another outfield bat could be filled this week, and portrayed the Yankees as being in the drivers' seat in terms of negotiations.
"It could happen when I decide, 'Yeah, I'm ready to commit,' " Cashman said. "I have players that are willing to move with me when I decide to."
The Winn move closes the door on any hope that Damon was returning for a fifth year with the Yankees. Damon hit .282 with 24 homers and 82 RBIs during the 2009 regular season.
"Johnny's going to be missed," manager Joe Girardi told WFAN on Wednesday. "He was great in the clubhouse, great on the field and, of course, in the playoffs last year. It didn't get worked out. I talked to Johnny. I wished him good luck and I thanked him for what he has done for our organization, and [told him] we're going to miss him. But I feel good about our outfield."
The 36-year-old Damon had been seeking as much as $13 million per season from New York, and negotiations never reopened after agent Scott Boras asked for two years and $20 million in December.
Various reports have suggested that Damon could wind up with the A's, Braves, Rays, Reds or Tigers, and he told the New York Daily News that there are "no hard feelings" with the Yankees.
"I loved my time in New York," Damon told the newspaper. "I thought it was the greatest organization. They ran everything the right way. I'm just glad we won, so I'll always be linked to a championship team in New York.
"I had discussions with [team president] Randy Levine, [Cashman] and [owner] Hal Steinbrenner, and we talked about how things are now in this economy in the baseball world. I understood their budget, and they understood where I was coming from. I wanted a two-year contract to come back and have a chance to win another World Series or two and see Derek Jeter get 3,000 hits."
Bryan Hoch is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.