The 700-year-old red light district is a big tourist attraction
The city has reached a 25m euro (£18m) deal to buy 18 buildings and turn them into shops or housing.
The mayor of Amsterdam, Job Cohen, said that although prostitution was legal in the Netherlands, there was too much of the sex trade in the city centre.
He also said that the trade involved exploitation and trafficking of women, and other kinds of criminal activity.
Prostitutes in Amsterdam's red light district ply their trade in neon-lit street windows and the area's seediness has always been part of its attraction for tourists.
Under the deal, 51 of these windows - a third of the total - will be sold.
The Wallen, as the area is known in Dutch, is in one of the oldest and most picturesque areas of Amsterdam.
But the city's authorities say the windows are a magnet for crime and money laundering.
Mr Cohen said the move was not intended to get rid of prostitution entirely, since it is part of the area's history.
"What we do want is to get rid of the underlying criminality," he said.
De Rode Draad
However, the plan was criticised by the Dutch sex workers' union De Rode Draad.
"We believe that less windows means more exploitation of women," spokeswoman Metje Blaak told Agence France-Presse news agency.
"If the windows close down, women who are being exploited will be hidden somewhere else where union representatives and health workers can't make contact with them," she said.Prostitutes hire the windows for around 100 euros (£70, $141) for part of the day. One window is usually used by several prostitutes a day.