The Orioles sent pitching prospect Zach Davies to the Brewers for Parra, a versatile outfielder who was hitting .328 with an .886 OPS, nine homers and 31 RBIs in 100 games this season in Milwaukee.
The deal was reached hours before the non-waiver trade deadline.
Parra, 28, is a .279 career hitter over parts of seven seasons with the Arizona Diamondbacks and the Brewers. He currently has a 14-game hitting streak, the longest active streak in MLB, according to ESPN Stats & Information. During the streak, he is hitting .460 with 13 runs scored.
The Orioles, who have been searching for an offensive upgrade, had been mentioned in speculation involving San Diego outfielder Justin Upton. But sources said the Orioles were resistant to include starter Kevin Gausman, minor leaguer reliever Mychal Givens or 23-year-old second baseman Jonathan Schoop in a trade for a veteran bat.
The Orioles entered the weekend with a 51-50 record, tying them for second in the AL East behind the New York Yankees. They're six games out of the division lead and two games out in the wild-card race.
Left field has been a problem for the Orioles this season. Travis Snider is batting .239 with three homers and 20 RBI, and Nolan Reimold has a .243 average with two home runs and seven RBI in 28 games.
Parra will probably take over as Baltimore's leadoff hitter. Manny Machado has been at the top of the order, but he's more of a power hitter and will likely be dropped to second or third in the lineup.
Parra has played all three outfield positions and is a two-time Gold Glove winner.
Davies is 5-6 with a 2.84 ERA in 19 games with Triple-A Norfolk. He was assigned to Triple-A Colorado Springs.
Baltimore cleared a roster spot by designating right-hander Bud Norris for assignment.
After going 15-8 with a 3.65 ERA last season, Norris signed a one-year contract with the Orioles during the offseason. He gave up eight runs in his first start and never really righted himself before going on the disabled list with bronchitis. He ultimately landed in the bullpen as a long reliever.
Norris is 2-9 with a 7.06 ERA. He yielded four runs and six hits in 2 2/3 innings on Thursday night in Baltimore's 9-8 loss to Detroit.
Information from The Associated Press contributed to this report.