That means Todd Redmond, who's "been pitching pretty damn good," will be moved out of the role.
"We'll give Redmond a little more work," said Gibbons. "We'll get him in some tougher situations and see what he does."
Mills made his big league debut for the Blue Jays in 2009, but he has moved around a bit in recent seasons. He was traded to the Angels in 2011 and claimed off waivers by the Rangers last season. Texas released Mills on July 18 of last season.
Mills has a career record of 4-4 with a 6.98 ERA in the Major Leagues. He signed with Milwaukee before this season and pitched to a 4-2 record and a 1.56 ERA for Triple-A Nashville. Mills was then acquired by Oakland for cash considerations in June, and he went 1-1 with a 4.41 ERA for the A's.
"He's a left-hander, a strike thrower, he can fit the long role for us," said Gibbons. "He adds some depth."
To make room on the 40-man roster, the Blue Jays designated pitcher Deck McGuire for assignment.
Jamie Ross is an associate reporter for MLB.com. Chris Toman is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.