Gardner, 23, has put pen to paper on an 18-month contract after the Spireites paid an undisclosed fee to secure his services.
Manager Paul Cook said: "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."
Commenting on the move, Gardner 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."
Gardner joined Celtic at the age of 18 and spent a year with the Glasgow giants. After a spell at Crewe Alexandra, he joined Droylsden before moving to Halifax in the summer of 2012.