After three days of talks, Mourinho agreed a three-year contract on a bumper salary reportedly worth more than USD 20 million a year.
But the 53-year-old Portuguese supercoach said it was the "mystique" of United that drew him to the challenge. United, one the world's biggest football clubs, need reviving after first David Moyes and then Louis van Gaal failed to emulate the glory years of Alex Ferguson.
"To become Manchester United manager is a special honour in the game," Mourinho said in a club statement.
"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.
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"I'm looking forward to being their manager and enjoying their magnificent support in the coming years."
Mourinho seemed destined to manage United ever since his Porto side eliminated Ferguson's men from the 2004 Champions League. Porto went on to win the title.
He thought his time had come when Ferguson retired in 2013, but concerns over his volatile personality prompted United to turn to the more reserved Moyes instead.
Media reports said Mourinho will earn up to USD 21 million a year.
- Challenge of remoulding squad -
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"Jose is quite simply the best manager in the game today," said United's executive vice-chairman Ed Woodward.
Mourinho was sacked by Chelsea in December but has
established a reputation as one of the best coaches in the game.
He has won league titles and cups in four countries with Porto, Chelsea, Inter Milan and Real Madrid. He won the Champions League in 2004 with Porto and in 2010 with Inter Milan.
The Red Devils' statement on Mourinho's appointment did not mention the future of Ryan Giggs, the club stalwart and Van Gaal's deputy who had been seen as a potential successor to the Dutchman.
Giggs, 42, knows the club inside out, has spent nearly three decades there as a player and then on the coaching staff.
Mourinho is expected to bring long-time assistant Rui Faria and goalkeeping coach Silvino Louro with him, meaning Van Gaal's assistant coaches Albert Stuivenberg and Frans Hoek are likely to be dismissed.
Former Paris Saint-Germain forward Zlatan Ibrahimovic, Sporting Lisbon midfielder Joao Mario, Everton defender John Stones, Chelsea midfielder Nemanja Matic and Atletico Madrid forward Antoine Griezmann are reportedly among the names on his wanted list.
But Mourinho might also have to deal with scepticism from the squad at Old Trafford after a report that some senior players have already expressed concern the tactically defensive coach might prove too similar to Van Gaal, whose tactics frustrated United fans.