The 20-year-old Spanish stopper completed his move from Atletico Madrid on Wednesday, having made a rapid rise through the ranks at Estadio Vicente Calderon.
He made his Rojiblancos bow in a Champions League tie at Porto in September 2009, aged just 18, before saving a penalty on his La Liga debut against Real Zaragoza.
"Edwin has been the best goalkeeper in the world whilst here at United," De Gea told Manchester United's in-house television station, MUTV.
"I hope to emulate him and spend a great number of years here. Hopefully I will equal or even surpass the performance and contribution he made to the club.
"The manager said that I should enjoy the holiday I've been afforded now, but of course I'm more excited about getting started in training and meeting my future team-mates."
"I am young but I'm coming here on the back of two full seasons in La Liga in Spain, so I think I've got enough experience to contribute to such a big club. I am planning to work extremely hard and do the best I can."
"There are differences between the two leagues. The Premier League is known to have a more physical style of play. There are a lot of high balls and a lot of play in the air but I hope to adapt fairly quickly and with my own style hope to contribute to it being an all-round success."
De Gea has already tasted glory during his short career, winning the 2010 Europa League and UEFA Super Cup with Atletico Madrid and this summer's European Under-21 Championships with Spain, and he is hungry for more honours.
"Of course everybody wants to win the Premier League. That's no different from me - I'd like to do that but also aiming to win the Champions League is realistic. That is what we're going to do."
