Gardner, 23, has penned an 18-month contract with the Sky Bet League Two promotion-chasing Spireites.
Manager Paul Cook told the club's official website: "I'm absolutely delighted to have signed Dan because he's a very exciting young prospect. We have watched him for some time and he's progressed really well at Halifax.
"He's a player who can make things happen in the last third of the pitch. We feel that we have got a very good squad and the signing of Dan makes it even stronger."
Gardner, who spent a year at Celtic as a teenager, said: "I'm very pleased because I wanted to play in the Football League and I think Chesterfield is definitely the best club for me to be at as they strive to win promotion to League One."