RIO DE JANEIRO (Reuters) - More than a million people thronged Brazil's Copacabana beach for a free Madonna concert on Saturday, braving the heat to see the end of her "Celebration" world tour.

The sand and oceanfront boulevard around Rio de Janeiro's famed beach were filled for several blocks by a crowd the city estimated at 1.6 million.

Many had been there for hours or even days to get a good spot, while richer fans anchored in dozens of boats near the beach and onlookers crowded beachfront apartments.

Firefighters sprayed water before the concert, when temperatures exceeded 30 degrees Celsius (86 degrees Fahrenheit), to cool fans gathered near the pop queen's stage, and drinking water was distributed for free. Temperatures were around 27 C (81 F) during the late night show.

Madonna, 65, performed songs such as "Like a Prayer", "Vogue" and "Express Yourself" for over two hours from 10:45 p.m. (0145 GMT on Sunday) as she wound up the greatest hits tour that started late last year.

"Rio, here we are, in the most beautiful place in the world, with the ocean, the mountains, Jesus," Madonna told the crowd, referring to the city's huge mountaintop Christ the Redeemer statue. "Magic."

Brazilian pop artists Anitta and Pabllo Vittar, as well as younger musicians from samba schools, participated in the show.

More than 3,000 police officers were deployed around the concert area, where the Rolling Stones and Rod Stewart have also drawn million-strong crowds. The authorities used a crowd-management strategy similar to their handling of the city's famous New Year's Eve celebrations.

Brazilian authorities have stepped up their vigilance over heat-related health problems after a young Brazilian fan died at a concert by Taylor Swift last year due to heat exhaustion.

Rio's state and city governments said they spent 20 million reais ($3.9 million) on the concert, while the rest was financed by private sponsors. The authorities estimate the concert could bring about 300 million reais to Rio's economy.

($1 = 5.0722 reais)