EXCLUSIVE By Duncan Castles Follow on Twitter
The Red Devils must now determine whether to sell De Gea this summer or to hold the Spain international to the final year of his contract, losing him on a free transfer at the end of next season.
The attraction of playing for the Spanish giants combined with the opportunity to return to his home city and residence of his girlfriend were significant factors in De Gea's decision to leave the Premier League.
United's handling of the 24-year-old in recent years – including Louis van Gaal's instruction that the club hold off on the offer of a new contract last summer until the incoming manager had time to work with De Gea in person – facilitated Madrid's approach.
It is understood that De Gea's advisors recommended that the Spaniard spend a further two years in English football before joining Madrid. Their argument was that the Premier League provides the best environment for an already highly capable goalkeeper to further develop in the position.
The allure of Madrid, however, proved irresistible to De Gea, and he has elected to follow Cristiano Ronaldo, Ruud van Nistelrooy, Gabriel Heinze and David Beckham in exchanging Old Trafford for the Bernabeu.
Signed from Atletico Madrid for a British record fee for a goalkeeper of £17.8million in 2011, De Gea was named United's Players' Player of the Year both in 2013-14 and 2014-15. He has won one Premier League title at Old Trafford and twice been named in the Professional Footballers' Association's Team of the Year.
Van Gaal signed former Barcelona goalkeeper Victor Valdes to United on an 18-month contract in January. During his first transfer window as Old Trafford manager, the Dutchman asked United to try to sign Costa Rica international Keylor Navas, but lost him to Madrid in a €10m transfer.
The United boss remains an admirer of a player who held his Netherlands side goalless for 120 minutes of their 2014 World Cup quarter-final and has included him on a list of potential summer replacements for De Gea.