The scheme, which was first launched in May, gives councils the chance to bid for grant funding at a special rate in an effort to allow them to more easily provide new homes based on social rent levels.
The largest sum was secured by Newham Borough Council, which landed £107m to build 1,123 homes.
The next highest was Ealing with £99m to construct 1,138 properties, followed by Southwark’s £89m for 926 homes.
Three councils signed up to the Building Council Homes for Londoners initiative at the time of its launch, with the mayor setting an initial target of 10,000 homes.
However, the mayor’s office said high levels of interest from boroughs had led it to increase the number of council house allocations to 11,154 homes.
The initiative also allows councils to ringfence their right-to-buy receipts to help them build homes to replace those sold in the local area.
The interest in Mr Khan’s programme follows the prime minister’s decision to abolish limits on the amount councils can borrow against their assets.
Mr Khan said: “Today, City Hall is using money we secured from government to help councils go much further.
“It is welcome that the prime minister has recently listened to calls that I and others have long made for councils to be able to borrow more to build.
“But let me be clear: lifting the borrowing cap for councils must be just the first step of reform, not the last.”
The mayor added that more money was needed to fund the building of homes required to solve the capital’s shortage of housing.
“We need at least four times the amount of money we currently get from government for new social and affordable homes, and we need far greater powers to step in and buy land for new council housing,” he said.
“The scale of what I have announced today shows the ambition is there in London to build a new generation of council homes; ministers now urgently need to step up and go the distance too.”
|London council fund allocation, highest to lowest|
|Borough council||Homes||Grant allocation|
|Kensington and Chelsea||336||£33,600,000|
|Barking and Dagenham||565||£25,338,000|
|Hammersmith and Fulham||251||£15,308,000|
|City of London||156||£14,880,000|
|Redbridge||400||(funding from right to buy receipts)|