The Spain international has moved to Old Trafford from Chelsea for £37.1million.
The 25-year-old should provide the creativity and invention which has been sadly lacking from David Moyes' team this season and he can not wait to play alongside Rooney.
"For me he is one of the best players in the history of this country," Mata said at his unveiling.
"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."
Asked about the pressure that comes with his price tag, Mata said: "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."
Mata surprised many by rejecting United's fabled number seven shirt in favour of the number eight recently vacated by midfielder Anderson, who has gone on loan to Fiorentina.
The seven shirt had been worn by Antonio Valencia, who changed to 25 at the start of the season citing the additional pressure in wearing a number previously graced by George Best, Eric Cantona, David Beckham and Cristiano Ronaldo among others.