Ayala and the Twins agreed to terms earlier this month, but the team had to make room on the 40-man roster. Right-handed reliever Bobby Korecky was claimed off waivers Wednesday by the Arizona Diamondbacks.
Ayala has a career record of 28-34 and a 3.44 ERA with 18 saves, 78 walks and 227 strikeouts in 339 appearances in six seasons.
He'll have a chance to be Minnesota's eighth-inning setup man.
Ayala reported to the Twins training camp on Sunday.