Allen told the club's official website: "Carl has quality and I'm delighted he's chosen us over four other clubs, including one from the Premiership.
"I believe I'm going to get the best out of him. I'm going to work him hard and push him to maximise his ability. Then the ball's in his court."
Cort, who has had his injury problems in the last few seasons, moves to the Walkers Stadium on a free transfer, having been released by Wolves.