The A's announced the deal Thursday before heading to Houston to begin a three-game series with the Astros. Blackley is expected to be on the Astros' roster for the series beginning Friday.
Blackley went 6-4 with a 3.86 ERA in 24 games for Oakland last season. He was designated for assignment last Friday after posting a 14.21 ERA in spring training.
Goebbert is a .285 career hitter with 31 homers and 237 RBIs in 456 games over four seasons in the minors.