Norwood's addition came at the expense of right-hander Alec Mills' roster spot. Mills wouldn't have been available for a few days after throwing six innings of relief in the Cubs' 11-1 loss to the Phillies on Wednesday evening.
Norwood threw one scoreless inning for the Cubs earlier this season. He had a 4.71 ERA in 39 appearances at Triple-A Iowa this season.
Mills had a 3.98 ERA in four appearances for the Cubs.