The 65,000 tickets for the central London gig went within minutes of being put on general release this morning.
AEG Live promoter Rob Hallett said the response had been “incredible”.
He said: “We sold 65,000 tickets in the speed the system could handle it. If the system could handle it in seconds, we would have probably sold out in seconds.”
Tickets cost £95, although there were hospitality packages for sale at up to £299 but Mr Hallett said basic ticket-holders would not lose out.
He said: “The band wanted the regular ticket-holders to be right at the front of the stage staring at the whites of their eyes, not 200 yards away.
“The people who have coughed up for hospitality packages will get looked after in a way they have never known before.
“But when the doors open, if you can run faster than the next guy, it will be like any other general admission gig. You will get down front.”
The band perform in Hyde Park in July – almost 44 years to the day they played a famous free concert in the central London park.
The band will also headline Glastonbury and play a north American tour this year.
Their first Hyde Park concert, on July 5 1969, was only two days after the death of founder member Brian Jones and marked the live debut of his replacement guitarist, Mick Taylor.
Guitarist Keith Richards said he hoped there would be “some emotion involved” in the new gig.
He said: “Not going to turn this into the funeral, but any more than that, I think it’s a celebration.
“I think that it’s a celebration for everybody really, for Brian, for everybody that was there and hopefully for loads of people that were not there the first time round.
“I’m really looking forward to it, it’s an exciting piece of news when I got the news that we were going to play the park again.”