Phelan had been in temporary charge for 12 weeks since Steve Bruce's departure in the summer, with the club currently 15th in the Premier League table.
A good start saw the 54-year-old named manager of the month for August.
In September, Phelan revealed he was offered the job on a full-time basis but there had since been no contact amid the club's search for a new owner.
"I'm very relieved," Phelan said on the club website. "It's been a while in coming."
Phelan added he was "looking forward" to the first full-time management role of his career, saying: "It's exciting to step over that threshold.
"I understand things are pending at this club so I am happy with that. I'm in charge of all football issues and that's what I needed to be clear."
The newly-promoted Tigers surprised many by winning their first two games of the season despite a summer of turmoil and stretched playing resources.
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Since then, however, they have gone five games in the league without a further win, picking up just one point. They have reached the fourth round of the EFL Cup, and travel to Bristol City next.
Former Manchester United assistant manager Phelan first arrived at Hull City in February 2015 when named assistant to Bruce, who this week was appointed manager at Championship side Aston Villa.
Hull, who have beaten champions Leicester and Swansea this season, visit Bournemouth on Saturday.
The club also confirmed on Thursday that Stephen Clemence had left the club to join Aston Villa as first-team coach under Bruce.
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Hull City have appointed caretaker manager Mike Phelan as their new head coach until the end of the season.