The 39-year-old, who managed the Spireites in 2017, is number two to new Hibs manager Shaun Maloney.
Former Celtic player Maloney, 38, moves to the Scottish Premiership club after leaving his role as Belgium’s assistant manager.
Caldwell played for Hibs and as well as managing the Spireites he has also been in charge of Wigan Athletic and Partick Thistle.
More recently, Caldwell had a spell as under-23 boss at Newcastle United and as loans coach at Manchester City.
On the appointment of Maloney, Hibs chief executive, Ben Kensell, said: “We wanted to acquire a manager who has an attacking mentality, who’s progressive, and someone who is hungry for the opportunity to build something here at this big club.
“Shaun has been the standout candidate throughout this process as his idea of football is completely aligned with ours and the history of this football club.”