Adrian Underwood, director of the Boarding Schools Association, said a few children already in care would also be considered for boarding-school places. Five councils will select 30 to 40 children for the pilot phase, which starts in September 2007. The councils will pay the school fees.
If the scheme is successful, the number of pupils involved could rise to 2,000 over the following few years.
"We will not be taking 14-year-olds from care with major psychiatric problems," Mr Underwood said. "We can't cope with that. The focus will be on children at risk of going into care."
Mr Underwood said that most children would be between the ages of eight - the youngest intake at boarding schools - and 13.
He said that although schools would be very unlikely to take children older than 13, it might be possible to offer a few sixth form places to 16-year-olds in care.
Jonathan Stanley, principal of the centre for excellence in residential care at the National Children's Bureau, said the scheme was interesting in principle.
"Training to meet the needs of these children will be essential in building up the confidence of staff at the schools," he said.
"They will also need training in how to work with other children's services."