Manchester, Sandwell, Leeds, North-east Derbyshire, Reading and London's Newham, Camden, Islington were told this week that their bids were successful.
The authorities will work up business cases for projects that will involve the transfer of run-down estates to private sector firms that will upgrade and maintain them for more than 20 years.
Under the PFI deals, a firm will, for example, put new roofs on an estate's buildings, and then guarantee their life for a number of years in return for money provided by the government. They will also be responsible for all other improvements and maintenance. Willmott Dixon and Tarmac are among the contractors understood to be leading the chase for PFI social housing deals.
The refurbishments became possible after a government decision to allow PFI in social housing last year.
Housing minister Hilary Armstrong made the first move, altering the regulations governing councils to allow them to transfer stock to PFI landlords in March 1998. She then committed to picking a series of pilot PFI social housing projects last September.
On 17 December, she wrote to councils around the UK inviting them to submit business cases for the new projects. These were submitted on 17 February.
Whitehall sources said the PFI route is seen as an improvement on the Housing Action Trusts introduced by the last government because it places less responsibility on tenants.
Although some tenants welcomed HATs, and the power to vote on whether to transfer an estate to a new trust, some tenants did not want to be involved.
"The new system would ensure tenants don't have to go through the agony of a ballot," one Whitehall source said.
Only major contractors are expected to benefit from the new PFI social housing route, because smaller firms will not be able to take on the significant risk the government hopes to transfer.
For example, a smaller contractor could not take on the cost of repairing hundreds of roofs it had promised to maintain if a defect was found in them years later.
But industry sources said smaller firms may yet benefit from PFI in social housing, because packages of work may be subcontracted to them by the bigger firm winning the overall bid.
One Whitehall source said: "Since councils were invited to bid, the key event was seen as the selection of councils. Now it has happened, PFI in social housing could become very big."