The Premier League champions announced the £37.1 million signing of the Spanish playmaker on Saturday evening.
It is a deal which it is hoped might give United's difficult campaign some impetus, with the team seventh in the league and out of both domestic cup competitions.
Talks are under way with striker Wayne Rooney to extend his agreement with the club, while there have also been reports of a bid for highly-rated Southampton left-back Luke Shaw as Moyes looks to put his stamp on the squad he inherited from Sir Alex Ferguson.
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."
The Scot admitted the signing had lifted the mood at Old Trafford.
He told MUTV: "Undoubtedly we could all do with a bit of a lift, we have not done as well as we would have liked to do. We see this as the start, we have to look to improve and I'm going to try to bring in some new players to make that happen.
"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."
Moyes, who said he would probably look to get Mata involved in Tuesday night's Premier League game against Cardiff, said it was a surprise that the deal was able to be done mid-season.
He added: "I never felt that we would get that opportunity, I wasn't sure that Chelsea would ever sell him to us. Thankfully we got there and I am delighted he is here.
"I'm a bit surprised because it's not something that tends to happen especially between Premier League teams. I was surprised when it happened but we have got a really exciting player, a player I'm looking forward to working with, a player I think everybody in football looked at and says he did a great job for Chelsea.
"I'm looking forward to seeing him in a red jersey and doing it for us."
Mata will be formally presented as a United player on Monday lunchtime at the club's training ground, but gave an interview to in-house channel MUTV in which he too expressed surprise that Chelsea had been prepared to let him go.
"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. The last six months were difficult for me, I didn't play as much as I wanted to," he said.
"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."
Mata revealed he had been in contact with United goalkeeper David de Gea, a team-mate at international level.
"He had been texting me the last five or six days, asking me 'when are you coming, when are you landing? Are you coming by helicopter or by bicycle?'," he said.
"At the end I am very happy to be with him. He's a very good friend and an amazing goalkeeper, so he is important for me."
Mata's capture - and Moyes' confidence that there will be more to follow - indicates the willingness of the Glazer family to invest in the squad in a bid to allow them to keep pace with title challengers Manchester City, Arsenal and Chelsea, if not this season then certainly in the future.
Mata insists he has come to United to add to his trophy collection.
"I would like to win the Premier League," he said.
"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."
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