Humber, who turns 28 on Tuesday, was 2-1 with a 4.15 ERA in eight games for the Royals last year. In his lone start, he gave up nine hits and five runs in 5 2/3 innings against the White Sox.
The 6-foot-3, 210-pounder was a first-round Draft pick of the Mets in 2004. He spent parts of two seasons with the Mets (2006-07), two seasons with the Twins (2008-09) and last year with the Royals.
In 51 1/3 career innings, he's posted a 2-1 record and a 5.26 ERA, with two starts.
Humber began last season at the Royals' Triple-A club in Omaha and went 5-6 with a 4.45 ERA in 21 games (20 as a starter), before being promoted to Kansas City on Aug. 5.
The A's 40-man roster is now at 39 players, with pitcher Rich Harden yet to be officially announced. Harden has agreed to terms on a one-year deal, but won't be officially added to the roster until he passes his physical.
The club also signed free-agent right-hander Brandon McCarthy to a one-year deal earlier in the week.