The former England international midfielder has been poised to sign the deal, which will be his first management job in football, for over a week.
NCM can confirm that the contract has now been signed and Ince will begin work at Moss Rose later today.
He takes over from 'Caretaker-manager' Ian Brightwell, who is expected to remain on the coaching staff, who had been temporarily holding the reigns after Brian Horton's departure in September.
Ince will have his work cut out, with the Shaymen yet to win a fixture this campaign.
Wise, with his Assistant Manager Gustavo Poyet, had looked set to take over the 'Championship' side, but the two clubs have failed to reach a compensation agreement. Swindon had earlier given Leeds permission to talk to Wise.
If Wise were to move,he will leave the County Ground with Swindon in third position. Leeds are currently second from bottom in their league.