The mayor of London will use funds from a £1.67bn pot he secured from the government in its spring statement to increase the number of homes in the capital.
He is also allowing London councils to bid for grant funding at a special rate, which will allow them to offer new homes based on social rent levels more easily, his office said.
Mr Khan criticised the government for failing to give councils in London the freedoms they require to ensure homes sold under the Right to Buy scheme are replaced.
Since Right to Buy was introduced in 1980, 306,000 social homes have been sold by councils in London, according to the Ministry of Housing.
During the same time, only 62,000 new homes have been built at social rent.
Mr Khan said: “I grew up on a council estate and I know first-hand the vital role social housing plays in London.
"Council homes for social rent bind our city together, and they have been built thanks to the ambition of London’s councils over many decades.
“Back in the 1970s, when I was growing up, London councils built thousands of social homes, providing homes for families and generations of Londoners.
"But the government has turned its back on local authorities, severely hampering their ambition to build by cutting funding and imposing arbitrary restrictions on borrowing."
Mr Khan added: “I am proud to launch Building Council Homes for Londoners – the first ever City Hall programme dedicated to new council housing.
"I want to help councils get back to building homes for Londoners again, and I’m doing that with support from the £1.67bn fund I secured from government to help get 10,000 new homes underway over the next four years.
“I am offering councils expertise and resources from City Hall to scale up their homebuilding programmes, and I will help them to replace homes sold through Right to Buy.
"The government is failing to enable councils to replace the hundreds of thousands of council homes sold through Right to Buy, and so I will do all I can to help councils replace as many of them as possible.”