Mata completed his move to Old Trafford from Chelsea late on Saturday night, having flown in by helicopter to the Aon Training Complex earlier in the day.
The Spain international has trained with his new team-mates for the last two days and fans could see him for the first time in a United shirt against Cardiff on Tuesday evening.
"I think no.8 is a great number," said Mata at an unveiling press conference at the Aon Training Complex on Monday.
"I like the number. I know seven is iconic here. I was speaking with David [Moyes] about it and we decided eight is a good number for me. Hopefully it will bring me luck."
The Reds' no.8 shirt was previously worn by Anderson, who made his debut for loan club Fiorentina at the weekend.