Baker is a career .271 hitter over parts of four seasons with the Marlins, although he was limited to 39 games over the past two seasons after having right elbow surgery in May 2010.
Baker is expected to back up Nick Hundley at catcher.
"Pre-injury, he was turning into a pretty good player," said San Diego general manager Josh Byrnes of Baker. "He had some power, had a good on-base [percentage] and good intangibles, like working with pitchers.
"We feel like our catching position is a lot stronger. Last year, when Nick was down, we were hurt by that."
Hundley missed 63 games with two disabled-list stints, first for a right oblique strain and later a right elbow strain that required minor surgery. Rob Johnson, Hundley's primary backup, hit .190 in 179 at-bats.
LeBlanc was 17-22 with a 4.54 ERA over parts of four seasons with the Padres, the team that drafted him in the second-round of the 2006 First-Year Player Draft. He was 5-6 and had a 4.63 ERA in 14 starts last season.
He was also 9-1 with a 4.30 ERA in 106 2/3 innings with Triple-A Tucson.
"It's kind of bittersweet," LeBlanc said Tuesday. "I enjoyed every second I spent in San Diego and with the Padres organization.
"They never once gave up on me. They gave me numerous opportunities. I wish I could have done better to establish myself for them. Hopefully it turns out being a win-win for both teams."
The Padres felt like they had enough starting pitching depth to make the deal involving LeBlanc, with more pitching on the way from the likes of Minor Leaguers Casey Kelly, Joe Wieland and Robbie Erlin, among others.
"We've got some depth," Byrnes said. "There were guys in front of LeBlanc and guys coming behind him. We've got a group there that can protect us."
Baker, who turns 31 on Jan. 20, appeared in 16 games last September after coming back from elbow surgery. He hit .154 in 13 at-bats. His best season came in 2009 when he hit .271 with nine home runs and 50 RBIs.
Baker, who had a sister graduate from San Diego State and still has a lot of extended family in the San Diego area, said playing last September after missing so much time essentially represented a career revival for him.
"It meant a lot. It's like getting called up again. To lose your childhood dreams because of something that's out of your control was tough," said Baker, who took a physical Tuesday in San Diego before returing to his home in Danville, Calif.
"To get back to the big leagues at the end of the season, it was like the first at-bat I had. I was so excited and so nervous. But it gave me some great perspective."
Baker, a native of Alameda, Calif., who played at the University of California, has a career .284 average and .365 on-base percentage against right-handed pitching, with 12 of his career 14 home runs coming vs. righties.
He is arbitration-eligible for the first time in his career.
One of Byrnes' primary goals this offseason is to improve the offense, especially against right-handed pitching.
Last season, the Padres ranked last in the Major Leagues in batting average against right-handers (.229), 29th in on-base percentage (.301) and 30th in slugging (.340). The Padres also ranked 28th in baseball in pinch-hitting (.161).
Byrnes and Marlins president of baseball operations Larry Beinfest first discussed a deal last week at the General Managers Meetings in Milwaukee.