The North-West outfit have paid a club-record £37.1m for the Spaniard, who dropped down the pecking order at Stamford Bridge under manager Jose Mourinho.
While some have questioned whether Mata will be able to fit into the system at United, the midfielder has insisted that he will feature in any role handed to him by boss David Moyes.
"I would like to play anywhere," Mata said in a press conference. "To play, try my best, to assist and to score. I will do my best to grow and do what I can.
"It's a massive club and I'm really glad to be here. In the history of the Premier League it's the club with most trophies so I'm really happy about that.
"I like the pressure. I think it's good for a footballer to improve when people expect big things from you."
Mata could make his debut against Cardiff City at Old Trafford tomorrow evening.