Mata's signing has raised hopes of a turnaround at United who are down in seventh spot, 14 points behind leaders Arsenal and six off the Champions League places.
Manager David Moyes said Mata had trained with his new team mates and that he would decide on Tuesday whether to pick the midfielder against bottom club Cardiff.
Moyes added that injured trio Wayne Rooney, Robin van Persie and Marouane Fellaini were back in training, raising the prospect of a four-way boost for the club.
The Scot was delighted to have bought Mata, saying he had doubts the club could pull the transfer off.
"I'm thrilled," Moyes told reporters. "I got wind of it a month or two ago that it could be a possibility and never believed we could pull it off.
"When we got the sniff there was a chance Juan could be available we went after it right away."
Mata has not played since New Year's Day, where he showed his displeasure at being substituted early in Chelsea's 3-0 win at Southampton.
The match will see former United favourite Ole Gunnar Solskjaer return to Old Trafford as manager of Cardiff, having replaced Malky Mackay earlier this month.
The Norwegian said he would try to keep emotion out of the occasion despite having claimed a piece of club history when he scored the winning goal in the 1999 Champions League final against Bayern Munich.
"It's hard to say if I'll stay detached," he told The Sun newspaper. "You never know, sometimes it just catches you doesn't it, like when you do your wedding speech and stuff.
"But I'm not too much of an emotional guy so I don't think that will be a problem. I'm more professional than emotional."
EVERTON BOOST
Everton, boosted by Leighton Baines signing a new four-year deal, will look to overtake Merseyside rivals Liverpool in the race for a Champions League spot when they clash at Anfield on Tuesday.
Roberto Martinez's Everton are sixth on 42 points, one point and two league positions behind Liverpool.
Everton have not won at the home of their local rivals since 1999 and Liverpool defender Kolo Toure said they needed to keep that record intact to give themselves breathing space.
"We all know it's a massive game," said Toure. "It will be really intense but we really need to win.
"The top four is where we want to be. We're there now but we will only stay there if we win this game.
"Everton are doing very well and Tottenham are close behind us too. But we are playing well and everyone is really focused.
"Our target is to be up there and we want those three points. At home we have a very good record and we want to keep that going."
Fifth-placed Tottenham host rampant Manchester City on Wednesday hoping to keep their six-match unbeaten run under new manager Tim Sherwood intact.
The last meeting between the pair in November saw City, now one point off the lead in second place, score six goals without reply and signalled the beginning of the end for Andre Villas-Boas who was sacked less than a month later.
Spurs are a more cohesive unit but will need to shackle City's free-scoring strikers to have any hope of success.
Arsenal could be without midfielder Jack Wilshere for Tuesday's visit to Southampton who will be minus Dejan Lovren and Gaston Ramirez with ankle ligament injuries.
Dani Osvaldo, Southampton's record signing, is serving a two-week suspension after an incident in training.
Tuesday's other matches see Norwich City host Newcastle United, Swansea City entertain Fulham and Hull City travel to Crystal Palace.
On Wednesday, Aston Villa host West Bromwich Albion, third-placed Chelsea entertain West Ham United and Stoke City travel to Sunderland.
(Editing by Tony Jimenez)
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