The midfielder was pictured at the club's Carrington Road training complex on Sunday, with media reporting that a deal would be announced on Monday.
It will be the second time that Matic, who turns 29 on Tuesday, has played under Mourinho. The Portuguese first signed him when he was Chelsea manager, for 21 million pounds in Jan. 2014.
Matic, who had originally joined the Blues in 2009 before moving to Benfica in 2011, became an influential part of Chelsea's title-winning side under Mourinho in 2014-15.
However, the 32-times capped Serbian international was among those under-performing badly in Mourinho's final season at Stamford Bridge before becoming a regular as new manager Antonio Conte took Chelsea to another title last season.
This month Chelsea have signed Monaco midfielder Tiemoue Bakayoko and, probably sensing his place was under threat, Matic declined to sign an extension to his contact which had two years left to run.
At Old Trafford, Matic will be reunited with another former Chelsea midfielder Juan Mata and compete with Michael Carrick and Marouane Fellaini for a first-team spot.
Matic's arrival follows Mourinho's unsuccessful move for Tottenham Hotspur's Eric Dier as United seek to mount a serious Premier League challenge for the first time since the departure of Alex Ferguson in 2013.
United have already signed 30-million-pound defender Victor Lindelof from Benfica and paid Everton 75 million pounds for striker Romelu Lukaku.
($1 = 0.7614 pounds)
(Reporting by Neil Robinson; Editing by Clare Fallon)
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