The 20-year-old has signed a five-year contract with United after passing a medical earlier this week.
“I feel very proud and I can’t wait to start playing here,” said De Gea to MUTV.
“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.”