O'Flaherty, 28, is coming back from Tommy John surgery that limited his 2013 campaign to 19 games with the Braves, but he's expected to be healthy by midseason. He was 13-7 with a 1.99 ERA over 295 appearances with Atlanta over the past five seasons after opening his career with three seasons in Seattle.
The 6-foot-2, 220-pound southpaw compiled a 1.45 ERA in 161 appearances over the past three years, which is the lowest mark among Major League relievers with 125 or more innings pitched. O'Flaherty held opponents to a .220 batting average over that span, including .156 against left-handed hitters.
O'Flaherty's 0.98 ERA in 2011 made him the first Major League pitcher to produce a sub-1.00 ERA while making at least 70 appearances.
The addition of O'Flaherty bolsters an A's bullpen in which Sean Doolittle is the only returning left-hander, though the club also acquired Fernando Abad in a trade with the Nationals in November. Oakland has already added right-handed closer Jim Johnson and setup man Luke Gregerson this offseason.
In his eight-year Major League career, O'Flaherty has limited left-handed hitters to a .200 batting average and a .531 OPS in 542 plate appearances, while right-handers have hit .270 with a .717 OPS in 796 plate appearances.
O'Flaherty was 3-0 with a 2.50 ERA and a 0.94 WHIP in 18 innings for the Braves last year before being shut down on May 18. He underwent Tommy John surgery three days later after tests revealed a tear in his left elbow's ulnar collateral ligament.
Brown, 28, was reacquired from the Nationals for cash on Dec. 19 after going 2-for-12 (.167) with a home run and one RBI in 14 games during a September callup with Washington. He spent most of the season with Triple-A Syracuse, where he hit .254 with 19 home runs and 56 RBIs in 107 games.
Brown was originally drafted by the A's as a compensation pick following the first round of the 2007 First-Year Player Draft and was sent to Washington as part of the Josh Willingham trade following the '10 season.
Greg Johns is a reporter for MLB.com. Follow him on Twitter @GregJohnsMLB as well as his Mariners Musings blog. This story was not subject to the approval of Major League Baseball or its clubs.