The centre-back has been at the Isthmian League Premier side in West Sussex since 2020 after joining from Havant and Waterlooville.
Bognor have said in a statement that they have an ‘excellent’ sell-on fee should Cook move on from Chesterfield in the future.
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On signing, Cook said: “I wasn’t expecting this when I left my old club last season. When the interest came in, I was delighted, and I couldn’t wait to get going.
“When this came up, it was case of grasp it with both hands and go for it. I think I owe it to myself to prove to myself that I know I can play at this level.
“I’m thankful to Paul Cook and the coaching staff that they have seen something in me to give me this opportunity back at this level.
“I’m a bit of an old school centre-half. I like to block, I like to head the ball and make tackles. I feel I can play as well – stepping out with the ball. Hopefully I can show the fans what I can do here.”
He becomes the Spireites’ second summer signing after left-back Branden Horton, 21, joined on a free transfer from Doncaster Rovers earlier this week.
His former manager at Bognor, Robbie Blake, said: "It was only a matter of time before Joe stepped up a level with the quality he has. He had a slow start to our season but then just got better and better.
"Paul (Cook) has seen what a good player he is and he will suit the way Chesterfield want to play because he is a ball-playing defender and Paul encourages his players in that regard. He is tailor-made for them.
"We wish him all the best and we should say that both parties are extremely happy with the deal that has been made."
Rocks general manager, Simon Cook, added: "A mutually beneficial fee has been agreed with an excellent sell-on fee in place too."
Town are also expected to announce the signing of forward Michael Gyasi, 22, from King’s Lynn Town over the weekend.