The Spanish international winger, 25, joined the Premier League champions on Saturday for a club-record fee of £37.1m.
"I'm thrilled. I got wind a month or so ago that it could be a possibility. I never really believed we'd pull it off," Moyes told reporters at Mata's official unveiling on Monday.
"I didn't think the players we were interested would be available. When we got a sniff Juan could be available we went after it right away."
Mata has been given the number eight shirt for United.