The team made the announcement on Friday.
The 30-year-old Volquez went 9-12 with a 5.71 ERA in 2013 while splitting time with the San Diego Padres and the Los Angeles Dodgers. He made the All-Star team in 2008 when he went 17-6 for Cincinnati.
Barmes hit .211 with five homers and 23 RBIs in 108 games for Pittsburgh last season. The 34-year-old veteran is a career .246 hitter over 11 seasons in the majors.