Cambridge Education Associates - a consultancy which is also the largest contractor for school inspections - is the preferred bidder for Islington local education authority in north London. The contract will be awarded next month.
Some services of Hackney local education authority have already been privatised, but Islington will be the first to have most - probably all - services run by a private contractor.
Cambridge Education Associates beat competition from Nord Anglia - run by Britain's first education multi-millionaire, Kevin McNeany, and winner of the Hackney contract - and CfBT, a not-for-profit consultancy bidding with Essex local education authority.
Islington agreed that a private company should be called in after a report from inspectors said the authority was incapable of improving itself. The council's schools have been under public scrutiny since Tony Blair decided not to send his children to school there.
Brian Oakley-Smith, managing director of the Cambridge firm, said: "Our aim will be to work in partnership with Islington LEA staff, schools, parents and the community to help them to achieve the challenging standards they have set themselves. We believe there is much good practice to be built on, and that the children and young people of Islington can achieve standards comparable with any in the country." The company will share management of the council's education services from January.
Estelle Morris, the Schools minister, said: "The inspection and intervention process has played a vital role in addressing longstanding problems with local education authorities.
"The department and Islington are determined that this will mark a new beginning for the borough and raise expectations about the future of education locally." Ms Morris has said she expects services to be privatised in up to 15 more local education authorities.
Theresa May, Tory education spokeswoman, said: "This contract is not the answer. The answer is to give decision-making powers to the schools."