To make room on the roster, reliever Adam Russell was designated for assignment and catcher Jose Lobaton and reliever Juan Cruz were placed on the 15-day disabled list. Lobaton has a left knee sprain and Cruz has a right groin strain.
Cobb was scheduled to make his sixth major league start Monday night against New York's A.J. Burnett. His promotion was announced Saturday, but wasn't made official until a few hours before the game.
Russell was 1-2 with a 3.03 ERA in 36 appearances with the Rays this season.