Tribal Group, which took over education services in 2002 after Ofsted inspectors found the council was hindering schools' chances of improvement, will hand back control in August.
John Simpson, Tribal chief executive, said: "For the first time in Swindon's history not one of its secondary schools is in Ofsted's categories of concern. Every management area that Ofsted measures is at least satisfactory and many are highly satisfactory."
Just a third of the education functions of the authority in the south-west of England were carried out satisfactorily when it was failed by Ofsted.
Tribal's contract was due to end this year, and the Department for Education and Skills decided the local authority was ready to resume responsibility.
An education partnership board, which includes heads, governors and representatives from the DfES, will continue to advise the council in September. The director of education under Tribal, Hilary Pitts, transfers to the council.
Garry Perkins, Swindon's cabinet member for education, said: "The Department for Education and Skills is now positive that we have the infrastructure to move the town's educational standards upwards."
Officials in Southwark, south London, are also awaiting approval from the DfES to bring education services back in-house.
Their contract with Cambridge Education Associates, the company which stepped in after WS Atkins pulled out of the borough, also ends this year.
Between 1999 and 2002, 25 local authorities were judged to be failing and in need of intervention. Of these, 10 brought in private companies either to run all education services or to provide strategic management.
Haringey, in north London, was the first contract to end, with Ofsted praising the "good progress" made by Capita.
Another success is Education Walsall, the name Serco operates under in the West Midlands borough, and which achieved one of the largest ever improvements between inspections.
But failures have included Nord Anglia, which had to be replaced by a not-for profit trust in Hackney, east London.