The 25-year-old Spanish international has joined United for £37.1million from Chelsea and may make his debut against Cardiff on Tuesday.
The midfielder arrived at Chelsea in August 2011 and made a massive impact in his first two seasons but has featured more intermittently this term and has now been allowed to join United.
"Coming here is a great moment for me," said Mata when he was unveiled as a United player at a press conference on Monday.
"I feel very happy to be here and have the chance to play for a massive club.
"The last six months at Chelsea were a bit difficult for me but now I am really happy and looking forward to winning as many trophies as I can with this club. I am sure it is going to be a great period for me.
"Manchester United is a massive club, with fans all around the world and this will be a big challenge.
"But I like the pressure, I think it's good for a footballer to try to improve. People are expecting big things from me and I am looking forward to it.
"What I like the most about this club is the character. I think if another club were in this position in the league (seventh), I think it would be very difficult to come back and take first position, but this club can do it.
"I think this is a club which is going to be successful for sure and I am happy to play anywhere, I want to try to assist and score, and I will try my best to improve as a player, to grow."
Mata is particularly looking forward to linking up with United's England international forward Wayne Rooney.
"For me he is one of the best players in the history of this country," said Mata. "He is unbelievable, he can score and he can assist.
"I will try to connect with him as much as I can. I will try to find the gaps in rival defences, try to be in the positions I have to be in to assist the strikers."
There had been speculation that Mata might be given the famous United number seven short but he will in fact be wearing number eight.
"I like number eight," he said. "I know seven is an iconic number here but I was speaking with David (Moyes) about it and we decided eight is a good number for me. Hopefully, it will being me good luck."
United boss David Moyes admitted that he was surprised to have been able to sign a player of Mata's calibre.
"I'm thrilled," he said. "I got wind of it a month or two ago that there could be an opportunity but I never really believed we could pull it off.
"I've been saying in press conferences that I didn't think we'd get a chance to do much business in January.
"I didn't think players would be available but, when we got a sniff that there was a chance Juan could be available, we went after it right away.
"Congratulations to the club and (chief executive) Ed Woodward for getting the deal done.
"We said the summer window would be tough but we've had a chance to look at everybody and now we will be making changes. Juan is the first."
Agree with solskjaer99 (Manchester United)! and "moyesophiles" (I laughed out loud), fantastic term to describe those blind fanboys- the alright one