The 20-year-old from Atletico Madrid replaces Edwin van der Sar, who retired in May. De Gea signed four days after helping Spain's U-21 team win the European Championships in Denmark.
"I saw their interest as an extra motivation to work even harder to show off my ability," de Gea said on FIFA.com. "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."
Man U paid a transfer fee of about 18 million, ESPN.com reports.
