The club also invited infield prospect Rougned Odor to big league spring training.
Bard, 28, had surgery for thoracic outlet syndrome on Jan. 2 and made just two appearances last season in the big leagues thanks to a long stay on the disabled list. The club doesn't have a timetable for his return.
"Matt Harrison was pitching instructional league games 2½ months after his surgery," GM Jon Daniels said last week. "We'll see once he gets in and we get our arms wrapped around him.
"This is the time of year you take chances on guys. This is taking a chance on a guy with a pedigree of being one of the best at what he does."
Bard has a 3.67 ERA in 211 career appearances -- all with the Boston Red Sox. From 2009 to 2011, he had a 2.88 ERA with 213 strikeouts and 76 walks in 197 innings.
Galarraga, who lost a perfect game with two outs in the ninth on a blown call at first by umpire Jim Joyce in 2010, will get a chance to resurrect his career with Texas, where he made his big league debut in 2007.
He was traded to Detroit before the 2008 season and pitched for Arizona in 2011 and Houston in 2012. He was in the minors last season, going 6-8 with a 3.64 ERA in 32 Triple-A starts for the Reds and Rockies.
Odor (pronounced ROOG-ned oh-DORE), who is No. 64 on ESPN.com writer Keith Law's top-100 prospect list for 2014, will report to big league spring training for the first time.