The 22-year-old spent last season at the Spireites after joining from Woking in the summer.
Carter was the Cards' top scorer before heading to the Proact and now gets his big move to the EFL.
He joins Dino Maamria's men for an undisclosed fee.
He's the latest National League player to make the move into the Football League this season.
Amongst others, Daniel Udoh left AFC Telford for Shrewsbury and Serhat Tasdemir swapped AFC Fylde for Peterborough.