The former Manchester United assistant boss took over in July when former manager Steve Bruce, who was announced as Aston Villa manager on Wednesday, quit the Tigers due to a lack of transfer activity.
Phelan had been in talks over the permanent role for over a month with the 54-year-old confirming he had been offered the job in September, but no announcement was made amid on-going speculation over the sale of the club.
“It’s been a while in coming, but I’m happy with the position I am now in and looking forward to the challenge ahead,” said Phelan.
“It has taken time but things have to be done correctly with these matters. What is important now is that we move forward and help this squad of players be successful for this football club.
“It’s exciting to step over that threshold into management, and I’m looking forward to working with this group of players that has done so well so far.
“The support I have received from everyone has been magnificent and I want that to continue because the challenges ahead are huge. The fans have been excellent through the last few months and the players have given me their full backing.
“I’m looking forward to what is to come now so roll on the next few games.”
Despite the lack of first-team players available at the start of the season – they had 13 fit going into the opening game of the season against Leicester – Phelan began well, with two wins from three in August earning him the manager of the month award.
The job is Phelan’s first permanent managerial role in football after being Norwich caretaker boss in 2015 and spending 14 years among the coaching staff at Old Trafford.