Phelan had been in caretaker charge since the summer departure of Steve Bruce, overseeing seven Premier League games so far from which the promoted Tigers have picked up seven points.
It first emerged in September that Phelan had been offered terms by the club's owners, who have been in takeover talks with several separate interested parties.
An agreement has now finally been reached, with a statement from Hull on Thursday saying: "The Tigers are pleased to confirm the appointment of Mike Phelan as the club's new head coach on a permanent basis."