Mueller, 34, hit .295 with 10 home runs and 62 RBIs for the Boston Red Sox, but spent his early years with the San Francisco Giants, where current Dodgers general manager Ned Colletti was assistant general manager. Mueller also called Colletti last week with an endorsement for the hiring of Grady Little, who later was selected to manage the Dodgers.
"When I mentioned his name to Grady," said Colletti, "he couldn't say yes fast enough."
Mueller, a former American League batting champ, is the third free agent signed by Colletti, after shortstop Rafael Furcal and backup catcher Sandy Alomar Jr., with more likely to come.
One scenario the Dodgers have considered would involve free agent outfielders Kenny Lofton and Reggie Sanders. Colletti also confirmed making an offer to Nomar Garciaparra, but said he would need to talk to the player before asking him to play first base or the outfield.
As for first base, Colletti indicated that a platoon of Hee-Seop Choi and Olmedo Saenz is a tentative plan, because his primary focus now is shoring up the outfield and starting rotation.
He has interest in Johnny Damon, but said that a report that he would meet with the free agent outfielder this weekend was "premature."
Colletti said Mueller could bat "as high as second or as low as sixth" in a batting order that now has Furcal on top, J.D. Drew third and Jeff Kent batting cleanup.
Mueller is seen as a temporary solution at third base until the arrival of top prospect Andy LaRoche, who split the 2005 season between the Class A and Double-A levels, hit 30 home runs and was named the organization's position player of the year.
"Not every player comes to the big leagues playing the position they played in the Minor Leagues," Colletti said of LaRoche, a high school shortstop who played first base in the Cape Cod League two years ago. "He can do more than play third base. If Billy's productive and LaRoche is ready for the big leagues, we'll find room for him."
Mueller reportedly had a three-year offer from the Pittsburgh Pirates, but his comfort level with Colletti and Little is believed to have helped sway his decision.
Colletti, one day after trading away Milton Bradley, praised Mueller's intangibles.
"His character is as good as it gets," he said. "He's a positive influence on veterans and young players. He has the right approach and the right attitude. There were people in the San Francisco organization who thought he wouldn't play a day in the Major Leagues. His career speaks for itself. He's a character guy, a winner."
Mueller, 5-foot-10 and 180 pounds, is a switch-hitter known for contact and on-base percentage, although he slugged 19 home runs with 85 RBIs while hitting a league-high .326 and winning the Silver Slugger Award in his career year of 2003.
That capped a comeback from a serious injury to his left knee suffered in 2001 when he slid into the metal beneath the padding along the wall in foul territory at Busch Stadium, fracturing his kneecap. He has had four knee operations, two on each knee.
Mueller has appeared in the postseason during five different seasons, including Boston's World Series title run in 2004. He earned $2.5 million in 2005.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.