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.
By the end of 2009/10 De Gea had won his first major trophy, keeping goal as Atletico beat Fulham in the Europa League final in Hamburg.
And that experience will stand the 6ft 4in keeper in good stead when in comes to replacing Van der Sar - who won four Premier League titles and a Champions League during his time at Old Trafford.
"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."
As is often the case when a young player moves to the Premier League from overseas, some are already questioning how quickly De Gea will be able to adapt to life in English football, but the Spaniard says he is prepared for the challenge.
"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."
