Of those who voted, 67% (41,000) voted to remain with the council and 33% (20,000) wanted to transfer to an RSL. The turnout was 66% of those eligible.
The decision in Birmingham came after a vote in Glasgow, in which tenants decided in favour of the transfer of more than 83,000 council homes to Glasgow Housing Association.
Brumwell warned that the terms and conditions of staff in Glasgow council's housing department could now be under threat as the housing association would be able to impose new contracts on them.
The Birmingham vote should serve to reinvigorate campaigns against stock transfer
UCATT general secretary George Brumwell
He said: "The terms and conditions of workers will come under threat if services are privatised."
In Glasgow, 58% of tenants voted to transfer the housing stock to an RSL.
Glasgow Housing Association says it will spend £1.8bn on repairs over the next 10 years and demolish 11,000 properties. Sid Patton, chairman of contractors' trade body Scottish Building, said the vote in Glasgow would keep the Scottish construction market buoyant.