Gaub, 26, went 0-0 with a 6.75 ERA in four appearances for the Cubs in 2011.
In five Minor League seasons, Gaub is 12-12 with a 3.60 ERA in 171 appearances.
He has been added to the Rays' 40-man roster, but he will not be part of the 25-man Opening Day roster. The move brought the 40-man roster to its full capacity.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.