Singer Mick Jagger, 62, danced around the stage like a skinny teenager for the two-hour show on Saturday night, which featured songs from their early days in London 40 years ago and from their latest Grammy-winning album A Bigger Bang.
Police deployed more than 6000 officers throughout Rio, one of the most beautiful but violent cities in the world.
Officials had been worried about widespread thefts or trouble with the drug gangs that rule the shantytowns, called favelas.
Police Colonel Leonardo Tavares said: "Nothing serious happened, thanks to God. It was calm."
A fire department official said about 250 people were treated for exhaustion, drunkenness and other problems.
Paramilitary troops had occupied several favelas after rival drug gangs killed six people in the Rocinha shantytown on Wednesday.
A Bigger Bang tour
Tavares estimated the crowd numbered about one million people.
Thousands more milled around surrounding streets, drinking beer and holding impromptu parties.
Others watched from a flotilla of private boats in the bay and from hotel rooms along Atlantic Avenue, the main thoroughfare along the beach.
Concert goers were estimated
to number one million
With its reputation for decadence, drugs and debauchery, Rio was the perfect venue for the Stones, former bad boys of rock who transformed into a powerful business operation.
The Rio concert was part of the band's A Bigger Bang tour, which started in the United States in August and was the top-grossing rock tour of 2005.
Fans came from as far away as Japan and Europe for the show.
From the classic opening riff of Jumping Jack Flash, to the encore of Satisfaction, fans sang, tried to dance on the crammed 1.5km stretch of beach and chanted praise for craggy-faced guitarist Keith Richards.
A group of die-hard supporters from Minas Gerais state arrived at the beach at 9am so they could get as close to the action as possible.
Fans arrived from early morning
One fan, Carlos, said: "I just wanted to see the greatest rock and roll band in the world. This is history"
"I want to hear Gimme Shelter, Start Me Up and Wild Horses."
The band played the latter two songs.
The public was separated from the stage by an enclosure for 4000 VIP guests of the promoter, the sponsors and the band.
The enclosure aggravated Freda, a 30-year-old teacher who travelled from Sao Paulo to see the concert.
"Brazilians have been through a lot of hardship, so this is a gift for them.
It is free, so that is politically correct"
"It is always like this in Brazil, everything for the millionaires," she said.
At one point, a section of the crowd started an obscene chant directed at the VIPs, who included actor Rodrigo Santoro and Brazilian TV presenter and model Luciana Gimenez, Jagger's former lover and the mother of his six-year-old son, Lucas.
"Brazilians have been through a lot of hardship, so this is a gift for them," Gimenez said.
"It is free, so that is politically correct."
Rio de Janeiro city paid about $750,000 for the show, or about 16% of the cost, with the rest covered by telecommunications companies Claro and Motorola.
It was billed as the biggest rock concert ever, but a reported 3.5 million people saw a free show by Rod Stewart on Copacabana Beach on New Year's Eve 1994.