The 24-year-old said: "Every player dreams of being in the Premiership and, although it is difficult for me to leave Chesterfield because they have been so good to me, this is an amazing opportunity
"I want to repay the faith that Paul Jewell has shown by proving that I am good enough to play in the Premiership."
Spireites boss Roy McFarland praised the professionalism of Folan, who signed a new contract at the club in October after he caught the attention of higher division clubs.
McFarland said: "Although we are disappointed to be losing Caleb we are delighted for him and really hope his career now takes off.
"As a potential end-of-season Bosman transfer, Caleb was a top guy in signing a new contract earlier this season to ensure the club also benefited from any potential transfer, and this has now happened."