A statement on the United website confirmed that a deal for the 24-year-old should be completed by the end of the month.
''Manchester United have received a world-record, unconditional offer of £80million for Cristiano Ronaldo from Real Madrid.
''At Cristiano's request - who has again expressed his desire to leave - and after discussion with the player's representatives, United have agreed to give Real Madrid permission to talk to the player.
''Matters are expected to be concluded by 30 June. The club will not comment until further notice.''
Ronaldo has long been a target for the Spanish giants, whose president Florentino Perez vowed earlier this week to do ''everything possible'' to take the 24-year-old to the Bernabeu.
Cristiano Ronaldo's last game for United was the Champions League final defeat to Barca
It is now certain that a second era of "Galacticos" has begun at Madird, with news of Ronaldo's £80m deal coming in the same week Perez agreed a £59, deal to sign Kaka.
The news is bound to be greeted with some scepticism by United fans who have repeatedly been told no deal had been agreed for the sale of FIFA's world player of the year in the face of regular statements from Spain the former Sporting Lisbon star was bound for the Bernabeu.
It was even suggested Ronaldo would be due a £20m compensation fee from Real if the deal did not go through by June 30, the date United now state themselves is when they expect matters to be concluded.
As it now seems a matter of when, rather than if a world record transfer will be completed, Sir Alex Ferguson might wish to explain why he has gone back on his famous comment in December last year that he would not ''sell that mob a virus''.
It is the first time for many years United would have allowed a player to leave they were not happy about losing.
Yet some supporters may be pleased that at least another drawn-out transfer saga, such as the one 12 months ago, is not played out in public.
And, at least the money could be reinvested in a squad that almost, but not quite proved good enough to win back-to-back Champions League trophies, in addition to a hat-trick of Premier League titles.