Eveland, 28, has appeared in 100 games (59 starts) in seven seasons with the Brewers, Diamondbacks, Athletics, Blue Jays, Pirates and Dodgers. He has posted a 19-24 record with a 5.52 earned run average.
Last season, the left-hander made five starts for the Dodgers and allowed 10 earned runs in 29 2/3 innings (3.03 ERA).
In exchange, the Orioles sent pitcher Jarret Martin and outfielder Tyler Henson -- both minor leaguers -- to Los Angeles. They designated pitcher Willie Eyre for assignment to make room for Eveland on the 40-man roster.
Baltimore made several other moves Thursday, selecting pitcher Andrew Loomis and infielder Matt Sweeney in the Rule 5 Draft. It also sent minor league infielder Greg Miclat to the Rangers, completing last week's trade for catcher Taylor Teagarden.