The Spain international will be presented to the media on Monday following his club-record £37.1million signing from Chelsea.
He memorably won the Champions League with the Blues in Munich in 2012, but has never won a league title in his career.
Doing so this season would appear fanciful in the extreme, with Mata moving to a club in the midst of a difficult campaign, lying seventh in the league, but the 25-year-old wants to bring silverware to United.
"I would like to win the Premier League," he said in an interview with in-house channel MUTV.
"It's a very, very special trophy and I think at this club you can achieve anything. I am young and I have been lucky enough to win some trophies, but I want to win a lot more."
Mata, who is in line to make his United debut against Cardiff on Tuesday night, admitted he was surprised Chelsea were prepared to let him go midway through the season.
"To be honest I think it's a bit surprising, but I have to say I am really grateful to Chelsea - to the owner, to the people working in the club and to the fans," he said.
"The last six months were difficult for me, I didn't play as much as I wanted to.
"I understand that football is a team sport and I respected that situation. But the chance to come to Manchester United was a great chance for me to carry on with my career, they are a massive club."
The Spaniard was Chelsea's player of the year for the past two seasons and wrote an open letter to the club's fans on his official website, saying he would "never forget" their "affection".
United boss David Moyes revealed his delight in bringing a "really exciting" player to Old Trafford.
"I want to build an exciting team, I want to win and I want to give the supporters something to shout about - I've not done that often enough," he said.
To that end, Moyes promised the capture of Mata would be "the first of many" new arrivals this year.
Moyes said of signing Mata: "This is the first, and there will be many more to come in time. I want the quality of Juan to be the start of it.
"I don't think we will have any more (new signings) in January - I'm still working on it and looking to do so. But hopefully it will be the first of some new signings, some new players who will arrive, more likely in the summertime."
Talks are under way with striker Wayne Rooney to extend his agreement with the club, with reports suggesting he may be handed the captain's armband, while there have also been reports of a bid for highly-rated Southampton left-back Luke Shaw.