It was the third trade between the teams this offseason and the eighth in three years.
Brown, 28, was designated for assignment by Washington last week so the Nationals could make room on their roster for newly signed outfielder Nate McLouth. Brown has no options remaining, meaning there is a good chance he will make the club out of camp as Oakland's fifth outfielder.
Brown will have competition, though, in Shane Peterson and Michael Taylor, who is also out of Minor League options. Either player could be lost on waivers if not kept on the A's 40-man roster, which is now full.
Brown can play all three outfield positions and most recently hit .254 with 19 home runs and 56 RBIs in 107 games for Triple-A Syracuse, earning a September callup with Washington, where he batted .167 with one homer in 14 games.
In all, Brown appeared in 36 Major League games with the Nationals over three seasons and got 40 at-bats, recording seven hits and two home runs.
Jane Lee is a reporter for MLB.com. Read her blog, Major Lee-ague, and follow her on Twitter @JaneMLB. This story was not subject to the approval of Major League Baseball or its clubs.