"The Tigers are pleased to confirm the appointment of Mike Phelan as the club's new head coach on a permanent basis," said a Hull statement.
Phelan had been in caretaker charge of the club ever since fellow former Manchester United player Steve Bruce stepped down as the Tigers' boss in pre-season.
Under Phelan, an assistant to legendary United manager Alex Ferguson for many years, newly-promoted Hull have taken seven points from their opening seven Premier League games this term.
Hull's announcement caps an uncertain few weeks for Phelan, long thought of as the most likely full-time replacement for Bruce, with the club's owners in takeover talks.
"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."
Hull won their opening two games of the Premier League season, against Leicester and Swansea, and were then only beaten narrowly by Manchester United.
Their start to the season saw Phelan, 53, named the Premier League's manager of the month for August.
Hull then drew at Burnley and enjoyed EFL Cup wins at Exeter and Stoke.
However, their last three league games have ended in defeat, albeit the losses were to divisional powers Arsenal, Liverpool and Chelsea.
This will be Phelan's first stint as a full-time head coach or manager. He left Old Trafford when Ferguson retired as United manager in 2013 and then had a short stint on Norwich's staff in 2014 before becoming Bruce's Hull deputy early last year.
Hull, currently 15th in the table, are away to Bournemouth on Saturday.
Phelan will, however, now be without first-team coach Stephen Clemence, who is set to carry out the same role at Aston Villa following Bruce's appointment as the Birmingham club's manager on Wednesday.
Bruce was named as as the new boss of second-tier strugglers Villa after they sacked Italian manager Roberto di Matteo.
Villa, the 1982 European champions, were relegated from the Premier League last season and are now languishing in 19th place in the second-tier Championship.