United, seeking to replace retired keeper Edwin van der Sar, did not provide details of the transfer fee but local media has estimated it to be around £18 million. The club said the 20-year-old had passed a medical this week.
De Gea, who came through the youth ranks at Atletico before making his La Liga debut in 2009, arrives at Old Trafford fresh from helping Spain to win the European Under-21 Championships in Denmark last week.
He will be United's third signing since the end of the season as the champions have led the way in spending, having brought in defender Phil Jones and forward Ashley Young in a close season spree reported to be close to £50 million.
United manager Sir Alex Ferguson, who has spoken previously of the desire to sign an adequate replacement for Van der Sar in good time, targeted one of the continent's best young goalkeeping talents in De Gea.
When Danish goalkeeper Peter Schmeichel quit Old Trafford in 1999 the club struggled for six years to sign someone of a similar calibre, eventually settling on Van der Sar having passed up the chance to snap him up from Ajax years earlier.
Knowing the Dutchman planned to retire at the end of last season, when United won a record 19th English league title, Ferguson learnt from past mistakes and had already begun preparing for his top keeper's departure.
He signed 27-year-old Dane Anders Lindegaard last November and De Gea will now compete with him and Van der Sar's previous deputy Tomasz Kuszscak for the number one spot between the posts.
