The 19-year-old has agreed to stay for an initial month at Brunton Park and will go straight into the Cumbrians' squad for Saturday's home clash with Bristol Rovers.
Cooper, who made his first-team debut for the Tigers in August 2008, has made three first-team appearances this season.
Hull last week completed the signing of James Chester from Manchester United for an undisclosed fee after the 21-year-old central defender's loan spell at Carlisle.
Source: PA
Source: PA