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7 year oldThe midfielder, 28, becomes United's third summer buy after £31m defender Victor Lindelof from Benfica and £75m striker Romelu Lukaku from Everton.
United manager Jose Mourinho described Matic as a "team player" who has "everything we want in a footballer; loyalty, consistency, ambition".
Matic said he was "delighted" to be joining at "an exciting time".
The Serbia midfielder added: "To work with Jose Mourinho once again was an opportunity I couldn't turn down.
"I have enjoyed my time at Chelsea and would like to thank the club and the fans for their support. I cannot wait to meet my new team-mates and to start training with them."
Former Chelsea manager Mourinho spent £21m to sign Matic from Benfica for a second spell at Stamford Bridge in January 2014.
He had been valued at less than £5m when he left as a makeweight in a deal for defender David Luiz in January 2011, two years after he first joined the Blues in a £1.5m move from Slovakian club MFK Kosice.
Matic scored once in 35 Premier League appearances during Chelsea's title-winning 2016-17 season, also striking spectacularly in their FA Cup semi-final victory over Tottenham in April.
His exit had been expected after the Blues signed France international Tiemoue Bakayoko, 22, from French champions Monaco in a reported £40m deal earlier in July.
Italian champions Juventus were also understood to be keen on Matic.
In 2015, Matic was named in the PFA's Premier League team of the year, along with five other players from Chelsea's title-winning team.
According to Opta, he averaged nearly four tackles, made more than two interceptions and won eight duels - a 50-50 contest - per 90 minutes over the 2014-15 campaign.
However, last season Matic won only 278 duels, at an average of 4.77.
Last season, while Chelsea team-mate N'Golo Kante made an average of 3.64 tackles per 90 minutes - the fourth highest in the Premier League behind Liverpool's Jordan Henderson, Leicester's Wilfred Ndidi and Idrissa Gueye of Everton - Matic managed only 1.7.
The deal for Matic brings United's summer spending to £146m.
Almost £900m has been spent by Premier League sides so far in the summer transfer window, which closes on 31 August, and accountancy firm Deloitte predicts top-flight clubs will surpass the record £1.165bn they spent last summer.
Manchester City took their spending beyond the £200m mark by signing Monaco left-back Benjamin Mendy on Monday, while Chelsea have also spent more than £100m.
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