Catcher Nick Hundley and infielder Chase Headley also agreed to contracts for the 2012 season, along with pitchers Luke Gregerson, Tim Stauffer and Joe Thatcher, outfielder Will Venable and catcher John Baker.
Volquez, a 28-year-old righty hurler, was acquired in a five-player trade which sent Mat Latos to Cincinnati. He rose to prominence in 2008, going 17-6 with a 3.21 ERA in his first year with the Reds. Last season, he went 5-7 with a 5.71 ERA.
Quentin, a two-time All-Star and former Silver Slugger Award winner, was acquired from the White Sox in exchange for pitchers Simon Castro and Pedro Hernandez. The 29-year-old catcher has belted at least 21 home runs in each of the last four seasons. In 2011, he batted .254 with 24 home runs, a career- high 31 doubles and 77 RBI in 118 games.
Hundley, 28, hit a career-high .288 with nine home runs, 29 RBI and 34 runs scored in 82 games for the Padres last season. He batted .367 over the final 37 games of 2011 after returning from right elbow surgery in early August.
Headley, 27, posted a career-best .289 average in 113 games for the Padres last season. The switch-hitter added 44 RBI and 43 runs scored and hit .352 against lefties -- the second-highest mark among qualifying NL players.
Gregerson went 3-3 with a career-best 2.75 ERA and 34 strikeouts in 61 relief appearances for the Padres a season ago. The 27-year-old righty has 216 strikeouts against 68 walks in 213 career relief appearances -- all with the Padres.
Stauffer, also a righty, went 9-12 with a 3.73 ERA in a career-high 31 starts with San Diego in 2011. The 29-year-old was the Padres' opening day starter last season.
Thatcher, a 30-year-old lefty reliever, appeared in just 18 games for the Padres last year after undergoing shoulder surgery in May. He has posted a 4-6 record with a 3.36 ERA in 182 career relief appearances over parts of five seasons with the Padres.
Venable, 29, hit .246 with nine home runs and 44 RBI in 121 games with the Padres last season -- his fourth with the club.
Baker, who turns 31 on January 20, was acquired from the Marlins this offseason in exchange for pitcher Wade LeBlanc. The career .271 hitter missed most of the 2011 campaign due to surgery on his right elbow.