Outfielder Mitch Haniger and left-handed pitcher Anthony Banda were sent to the Diamondbacks.
Parra is expected to join the team Friday in St. Louis.
"The addition of Parra gives us a veteran player who helps to balance our lineup and also brings Gold Glove defense," general manager Doug Melvin said in a statement.
Parra, 27, is batting .259 with six home runs and 30 RBIs in 104 games this season. He has made 98 starts.
Signing as a non-drafted free agent on Aug. 30, 2004, Parra had spent his entire professional career in the Diamondbacks organization. He is a career .274 hitter with 39 home runs and 250 RBIs in 787 major league games (2009-14).
Parra, known for his defense, has won National League Gold Glove Awards in left field (2011) and right field (2013).
Haniger, 24, was selected by the Brewers in the supplemental first round of the 2012 draft. He batted .255 with 10 home runs and 34 RBIs in 67 games at Double-A Huntsville this season.
Banda, 20, was selected by the Brewers in the 10th round of the 2012 draft. He was 6-6 with a 3.66 ERA and two saves in 20 games (14 starts) at Class A Wisconsin this season.
To make room for Parra on the 25-man roster, outfielder Logan Schafer will be optioned to Triple-A Nashville.