After months of rumours, the Stones announced on Monday that they would play two nights at London's 02 Arena on November 25 and 29, followed by gigs at New Jersey's Newark Prudential Center, just outside New York, on December 13 and 15.
But hundreds of fans have taken to the Internet to complain about the ticket prices, with a seat for the London shows costing £406 ($650, 500 euros) on the official ticket website.
Premium tickets have subsequently appeared on re-sale websites for more than £13,000 each.
The cheapest seats on the official site, costing £106, appeared to be sold out on Wednesday.
"These prices are a joke," fan Steve Grace wrote in a comment appearing on the official See Tickets website. "To expect this sort of money just makes me lose a lot of respect for these guys."
Drachan Forster added on the site: "Saw them in Rio at a free concert. Was pickpocketed relentlessly throughout, but nothing compares to this fleecing. £246 for some of the worse seated tickets in the house. Disgusting."
By Wednesday, seats at the front of the 20,000-capacity 02 Arena were listed on the Get Me In re-sale website for up to £13,200 each.
Many fans protested online that the band should have rewarded their fans for their loyalty over the last half-century with cheaper shows.
"Considering these guys started off as a working-class set of lads, these prices are well out of reach of the ordinary working man," Chrissi Matusevics posted on Facebook.
American Express customers gained advance access to tickets for the London shows on Monday, followed on Wednesday by subscribers to the band's mailing list and users of Britain's O2 mobile phone network.
The tickets go on general sale in Britain on Friday.
Hospitality package tickets for the two US shows go on pre-sale on Saturday, ahead of a wider pre-sale next Monday and a general release on October 26.
Frontman Mick Jagger, 69, told BBC radio on Monday that the four concerts will be followed by a longer string of dates, yet to be announced.
US music magazine Billboard reported in August that Jagger and bandmates Charlie Watts, Keith Richards and Ronnie Wood will earn a total of $25 million for the four shows.