The 20-year-old goalkeeper passed a medical this week and has agreed a five-year deal with the club.
“I feel very proud and I can’t wait to start playing here,” said De Gea in an exclusive interview with MUTV, to be shown on the channel at 18:30 BST today.
“When a club the size of Manchester United comes in for you it obviously makes you very, very happy.
"I saw their interest as an extra motivation to work even harder to show off my ability.
"It’s a great privilege to be part of a club like United and I'm keen to do my best and show what I can do.”
The young stopper, who was part of Spain’s victorious squad at the UEFA European Under-21
Born: 7 Nov 1990
UEFA Europa League: 2010
UEFA Super Cup: 2010
UEFA European Under-17 Football Championship: 2007
FIFA U-17 World Cup Runner-up: 2007
UEFA European Under-21 Football Championship: 2011