The 53-year-old has been strongly linked with the position over the last couple of months and speculation grew when Louis van Gaal was relieved of his duties following the 2015-16 campaign.
After the final negotiations were concluded, Mourinho travelled to Manchester to sign a three-year contract with an option to stay at the club until at least 2020.
"To become Manchester United manager is a special honour in the game. It is a club known and admired throughout the world. There is a mystique and a romance about it which no other club can match," Mourinho told the club's official website.
"I have always felt an affinity with Old Trafford; it has hosted some important memories for me in my career and I have always enjoyed a rapport with the United fans. I'm looking forward to being their manager and enjoying their magnificent support in the coming years."
Man United executive vice-chairman Ed Woodward added: "Jose is quite simply the best manager in the game today. He has won trophies and inspired players in countries across Europe and, of course, he knows the Premier League very well, having won three titles here.
"I'd like to take this opportunity to welcome him to Manchester United. His track record of success is ideal to take the club forward."
Mourinho has won 22 trophies since 2003 and has managed at the top level of European football for over a decade. He led Chelsea to the 2014-15 Premier League title, but left Stamford Bridge in December 2015 after the champions lost nine of their first 16 league games.