The two sides agreed to a $675,000, one-year deal, according to multiple reports.
Gwynn, an outstanding defensive player, is expected to share time in left field with veteran Jay Gibbons, although Gwynn likely will get the bulk of the starts.
Dodgers general manager Ned Colletti said in his daily winter meetings briefing with reporters that he had made considerable progress toward signing an outfielder, but he declined to identify that player and later didn't immediately respond to a text message seeking confirmation that it was Gwynn.
However, Colletti did offer enough hints to point in Gwynn's direction.
"It's not a big-time bat or anything that is going to shock the world," Colletti said. "But it is somebody I think we really, really need."
Colletti later conceded that the player had two traits the Dodgers needed in speed and defense. Gywnn, 28, who grew up in Poway, Calif. while his father starred for the San Diego Padres, has been a part-time player throughout his five major league seasons and has never reached 500 plate appearances in any one year. He has almost no power, his five career homers all having come during the past two seasons with the Padres, and his stolen-base numbers aren't exactly eyepopping -- he stole a career high 17 in 21 attempts in 2010.
Gwynn became a free agent when the Padres chose last week to non-tender him rather than go to arbitration. Gwynn would have been a first-year arbitration-eligible player after making just $419,800 last year. Financial terms of his new deal weren't immediately available.
Tony Jackson covers the Dodgers for ESPNLosAngeles.com.