The midfielder was helicoptered into the Aon Training Complex on Saturday morning before completing his medical and agreeing personal terms.
And manager David Moyes has already confirmed Mata will be in his squad for Tuesday's Premier League encounter with Cardiff at Old Trafford.
"I know our fans have admired Juan for some time now - he has always played well against us - and I know they will be delighted to see him in the red of United; starting on Tuesday," said Moyes.
The sum spent on Mata smashes United's previous record outlay - the £30.75million they paid Tottenham for Dimitar Berbatov in 2008.
It underlines the desperation at Old Trafford to prove they are determined to shove United back to the top end of the Premier League after this season's disastrous campaign.
United have slumped to seventh in the table and were eliminated from the Capital One Cup semi-finals by 19th-placed Sunderland on Wednesday.
In addition, they have also been knocked out of the FA Cup, meaning an unlikely Champions League triumph is now their only hope of silverware, in addition to currently being their best route back into the competition next term.
Nevertheless, despite the strife, Mata had no hesitation in jumping at the chance to rebuild his career, which has stalled following Jose Mourinho's arrival at Stamford Bridge, even though he was crowned Chelsea's player of the year in the previous two seasons.
"I am thrilled to be joining United,'' he said.
"I have enjoyed some very happy years at Chelsea but the time has come for a new challenge.
"United is the perfect place for me and I am excited at the chance I have to be part of the next phase in the club's history.
"Chelsea is a top club and I have many friends there but you cannot turn down the chance to join Manchester United.
"I look forward to helping the manager and the team be successful in the coming years.''
Mata is ineligible for Europe, meaning his task for the remainder of this season will be to inspire a team whose recent performances have been appalling by their own high standards.
Moyes has clearly noted a lack of invention in his squad, which has only been accentuated by the recent absences of Robin van Persie and Wayne Rooney.
And having been a regular for Spain - one of the major reasons behind Mata's desire to move was to cement a place in his country's World Cup squad next summer - he has the experience and ability to have the kind of instant impact Moyes craves.
"Juan is one of the finest playmakers in the game today and it's a real pleasure to have secured his signature,'' said Moyes.
"He's been instrumental in Chelsea's recent success, with a notable 28 assists and 32 goals in his last two Premier League seasons.
"I have been impressed with the excitement he has shown to be part of the new Manchester United.''
Moyes can only hope to have more success with Mata than his first major signing as United boss, Marouane Fellaini, who has struggled badly for form and is now nearing full fitness again after a recent wrist injury.
With Sir Alex Ferguson underlining an intention to stick with the man he personally put forward to replace him last summer, the Glazer family are evidently going to provide Moyes with the funds he so desperately needs to reinforce an ailing squad.
It is thought a large bid for Southampton full-back Luke Shaw could be tabled prior to the transfer window closing next Friday.
And overtures are now being made to Rooney over a lengthy new contract extension the club hope will effectively tie the 28-year-old down for the
remainder of his career.
If executive vice-chairman Ed Woodward can bring those negatiations to a successful conclusion, it would represent a clear statement of intent on United's behalf considering Rooney was looking for assurances over the commitment to bringing in top quality players when he slapped his infamous transfer request in during the 2010-11 campaign.
Whilst Ferguson dismissed those comments, and delivered two more championships in response, it is unlikely Rooney's demands will have changed and it is hard to see him signing any contract without receiving some kind of assurances for the future direction of the Red Devils.
@JacobBurns> United fans complain was that sugar daddy clubs spent cash they didn't have. United are spending their own cash.- Synergy
Lastly the best part of this transfer is that we United fans get to watch one of the best playmakers in the world ply his trade for us during his prime. Thank you Jose, we really appreciate this late Xmas gift.