The 25-year-old Spain international, who had fallen down the Stamford Bridge pecking order under Jose Mourinho, has completed a club-record move to Old Trafford
The Spain international missed first-team training with the west London outfit on Wednesday as he closed in on the club-record move to the reigning Premier League champions in a deal worth £37.1 million.
Jose Mourinho has already moved to secure a replacement for the Spaniard, as the Blues gazumped Liverpool to agree a fee with Basel for Mohamed Salah, a transfer which could cost up to £15m.
Speaking about the deal, Mata said he was delighted to have joined the reigning Premier League champions, describing Old Trafford as the "perfect place for me".
"I am thrilled to be joining United. I have enjoyed some very happy years at Chelsea but the time has come for a new challenge," he told the club's official website.
"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."
David Moyes, meanwhile, confirmed that Mata will make his United debut against Cardiff on Tuesday at Old Trafford.
"I have been impressed with the excitement he has shown to be part of the new Manchester United," he added.
"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.
"Juan is one of the finest playmakers in the game today and it's a real pleasure to have secured his signature," he added.
"He's been instrumental in Chelsea's recent success, with a notable 28 assists and 32 goals in his last two Premier League seasons."
Mata, twice named Chelsea's Player of the Season, struggled for regular football under Mourinho, with the Portuguese recently admitting his "door was open" should the playmaker seek an exit.
And United have jumped at the opportunity to bring the 25-year-old to Old Trafford, with David Moyes keen to boost his midfield options and strengthen the club's bid to claim Champions League qualification after the disappointment of crashing out of the Capital One Cup.