Torrealba receives a two-year deal for $6.25 million, with $3 million of it coming in the first year and $3.25 million in the second.
"I was looking for a team that could compete and hopefully make it to the playoffs," Torrealba said Monday. "I'm really excited with this bunch of talented young pitchers here. I want to help them out as much as I can by the way I call the game and take charge."
Torrealba, 32, batted .271 with seven home runs and 37 RBIs in 95 games for the Padres last season. He started 89 games, and the Padres were 53-36 in those games with a 3.14 ERA, the lowest to a catcher in the majors since the Los Angeles Dodgers had a 2.73 ERA with Paul Lo Duca behind the plate in 2003.
He's a career .257 hitter in 10 seasons with the Giants, Mariners, Rockies and Padres.
Rangers assistant general manager Thad Levine said the team expects its starting catcher to play in 95-110 games, considering the rigors of the Texas summer heat. Torrealba doesn't anticipate difficulty.
"Obviously the weather is different than where I played before," the catcher said. "I really believe so. I should be able to do it."
Molina was acquired at the trade deadline last season from the Giants and stabilized the catching position as the Rangers made a run to the World Series. Texas did not offer Molina arbitration.
Molina, who played 61 regular-season games for the Giants before 57 in Texas, still gets a championship ring after San Francisco beat the Rangers in the World Series.
Molina has hinted at retirement, though general manager Jon Daniels said last week there are indications that the catcher would like to play another season.
Levine said the Rangers were interested in having Matt Treanor, who split time behind the plate with Molina, return next season. While Treanor hit only .211 in 82 games, he was a steady influence working with pitchers and in the clubhouse.
The team also agreed to terms with reliever Mark Lowe on a one-year, $1.2 million contract on Monday.
Lowe will also receive $100,000 in additional incentives. The deal, first reported by MLB.com, means the sides avoid going to an arbitration hearing.
Lowe, 27, was part of the Cliff Lee trade in July. The reliever had back surgery in May and returned for three games near the end of the regular season with the Rangers.
He was not on the postseason roster for the ALDS or ALCS, but was placed on the World Series roster. He struggled in his two appearances against the Giants, giving up five runs on four hits with a walk in two-thirds of an inning.
When healthy, Lowe gives the Rangers another power arm in the late innings. He touched the mid 90s on his fastball at the end of the season and is used to pitching in tight situations. In 2009 for Seattle, Lowe had a 3.26 ERA with 26 holds in 80 innings.
Information from ESPNDallas.com's Richard Durrett and The Associated Press was used in this report.