The Chelsea midfielder flew north on Saturday and is expected to train with his new team-mates on Sunday.
The final paperwork on United's club-record deal cannot be completed until Monday, but Mata has now undergone a medical assessment.
And United players have already begun welcoming the Spain international via their Twitter accounts.
Rio Ferdinand wrote: "Welcome to my amigo Juan Mata! Hoping you enjoy ya time here and help continue the success at this club."
And Robin van Persie wrote: "Welcome Juan Mata. See you all Tuesday."
A photo on United's Twitter feed on Saturday showed David Moyes greeting Mata, who arrived by helicopter at the club's Carrington training ground.
United and Chelsea have already reached agreement over the transfer, which will far exceed the £30.75m deal for Dimitar Berbatov in 2008.
The fee also represents a hefty profit for Chelsea on a player they signed for £23.5m from Valencia in 2011.
Speaking at his Friday afternoon press conference, Chelsea boss Jose Mourinho wished Mata well.
He said: "He's a fantastic player and despite not playing a lot for us in the last period could be a very important player for us. But Juan had this fantastic opportunity for him.
"It's what he wants. It's what he asked us to accept. Chelsea Football Club is proud to act this way, in an open way, in a human way."
Mata was named Chelsea's player of the year in each of the past two seasons but has been reduced to a bit-part role since Mourinho returned to Stamford Bridge.
"The offer we've received we feel is the right offer for the quality of the player," Mourinho said. "It's a good move for Juan, it's a good move for the Premier League and the offer is the right offer. He was fantastic for Chelsea, and Chelsea were fantastic for him."
Responding to criticism of the sale from some supporters, he said: "If the fans are sad that Juan is leaving, I will say that we are also sad. No one is jumping around the place."
Mata's replacement in the Chelsea squad will be Mohamed Salah, subject to a successful medical.
Salah has agreed personal terms, but Mourinho explained that he will have to have his medical - the last step in the deal to sign him from Basel - in Switzerland.
"He's a non-EC player. He cannot come to England for his medical, so we have to travel to meet him and to have the medical, probably in Switzerland. Only after that can we do the paperwork to bring him to the country," said Mourinho, who is excited by the signing.
"I like the fact that he can play the same way our attacking players do, which is players with adaptability, to play right, left, or behind the striker.
"He's young, he's fast, he's creative, he's enthusiastic. When we analysed him he looks the kind of humble personality on the pitch, ready to work for the team and to work and to adapt himself to a new life.
"We believe if he comes that he will have a similar process to the Willian one. Willian needed two or three months to grow up and to feel comfortable playing for us (following his August signing from Anzhi Makhachkala).
"We think with him and (Andre) Schurrle, (Eden) Hazard, Oscar and Willian we will be fine.
"We lose an experienced top player like Juan, but we bring in a young player with great potential.
"Willian did that transition from his previous world to the top world of football. Hopefully, if Salah comes, he can do the same. We are ready to help, we are ready to support.
"He has some experience in Europe, the Europa League, Champions League, so he's not a naive boy arriving in the jungle.
"Hopefully he comes and hopefully with the talented players we have around in the same positions we all can develop together."