United released a statement saying Mata will move for a club-record fee "subject to a medical and the agreement of personal terms."
Although United didn't give any further details, the club this week made a bid of 37 million pounds ($61 million) for Mata, which would eclipse the 30.7 million pounds that United paid to sign striker Dimitar Berbatov from Tottenham in 2008.
Chelsea manager Jose Mourinho said Mata had requested to leave Stamford Bridge after losing his place in the London club's starting lineup.
"I asked him (Mata), 'Are you really happy to go?'" Mourinho said. "He said, 'Yes, I'm really happy to go.'
"We hope he does well," Mourinho added in a news conference. "We are convinced he is going to do well. If Man United pays their record for a player, it's because they know exactly what they want from him. And they know exactly what he can give them."
The 25-year-old Mata was Chelsea's player of the year for the last two seasons but has been marginalized at the London club this campaign following the return of Mourinho as manager.
He has largely been on the bench, with Mourinho preferring Eden Hazard, Willian and Oscar as his playmakers.
"If he cannot be fully happy here because he is not playing 100 per cent like he was the last two years, if he has a big club that wants him — even if it's a rival club and in England — the club decided, and I was on the club's side for this feeling, that you cannot stop people to be happy," Mourinho said.
United refused to negotiate with Chelsea in the off-season when Mourinho lodged two bids for Wayne Rooney, who was pushing for a transfer after losing his regular place in United's team.
Mourinho said that hadn't been a factor in dealing with Mata.
"Would Chelsea supporters be happy if we stop a fantastic person, that they all like, from being happy, if we say you only can go to Russia, China, to France or to Portugal, not England?" Mourinho asked.
"To say now, 'You cannot go, Juan, to United because United refused in the summer to sell us Wayne Rooney,' I don't think it's fair to Juan. So if they decide not to sell (Rooney, it's) their decision."
United will hope the arrival of Mata, who is likely to be in Spain's squad for the World Cup in Brazil, proves to be a turning point in its so-far lacklustre season under new manager David Moyes.
The team is languishing in seventh place in the Premier League — 14 points behind leader Arsenal — and facing a fight to secure one of the four Champions League places.
United exited the FA Cup at the first hurdle and the League Cup in the semifinals.
The bright spot is still remaining in Champions League title contention going into the round of 16 against Olympiakos next month.
Chelsea, meanwhile, has already found a replacement for Mata in Mohamed Salah after striking a deal with Swiss team Basel for the pacey Egypt winger.
Salah still needs to agree personal terms and pass a medical with Chelsea.
Mourinho laughed off criticism by Arsenal manager Arsene Wenger, who said Thursday that Chelsea had timed the sale of Mata specifically to hurt its Premier League rivals.
United has already played Chelsea twice — most recently on Sunday — but still has to play Manchester City and Wenger's Arsenal in the run-in.
"Wenger complaining is normal, because he always does. It's something that we know," Mourinho said. "We don't do the market, we don't do the rules."
Two points separate Arsenal with third-place Chelsea with 16 games left.