Security company G4S is to sell its children's services business including the contract to manage two secure units - one at the centre of abuse claims.
The centres are at Oakhill, Buckinghamshire, and Medway, Kent. The sale - as part of a business review - includes its 13 children's homes.
A BBC Panorama investigation uncovered claims relating to the treatment of 10 boys at the Medway unit near Rochester.
The director of the facility stepped down at the end of January.
Undercover footage showed staff mistreating and abusing inmates, and boasting about using inappropriate techniques to restrain youngsters.
Other allegations included claims staff tried to hide their actions by ensuring they were out of shot from CCTV cameras.
Five men were arrested by Kent Police on suspicion of either child neglect or assault and bailed until April.
G4S sacked five members of staff. Three others are currently suspended.
The company runs residential children's homes through its children's services division, Homes2Inspire, in six English counties: Bedfordshire, Derbyshire, Northamptonshire, Nottinghamshire, Oxfordshire and Staffordshire.
It also has a contract to run Rainsbrook secure training centre in Northamptonshire, which is currently being transferred to a new provider, MTC Novo.
A G4S spokesman said there had already been "a number of expressions of interest from parties" interested in buying the children's services business.
The company hopes to complete the process by the end of the year.
He said it would consider selling off the secure training centres individually or as part of a package with the children's homes.
The BBC's Home Affairs correspondent Danny Shaw said: "It's thought three of the providers that are expected to be in the running to take over the children's service contracts from G4S are Diagrama, originally founded in Spain; Ingeus, which runs probation services; and MTC Novo, which is taking over the Rainsbrook contract."
The announcement was welcomed by Andrew Neilson, director of campaigns at the Howard League for Penal Reform.
"These child jails have been the focus of much controversy... there is now an opportunity developing to close the secure training centres down completely.
"These centres are a failed model and this wise withdrawal from the market by G4S should not be followed up new private security companies coming in to replace them, with dubious track records abroad in the treatment of people in custody," he said.