Classes in a variety of subjects will be broadcast for four hours, six days a week, on 41 radio stations and the country's sole TV channel, the government announced.
"The plan is to provide a suitable option for our school-going population as the entire school system has been disrupted since the outbreak of the Ebola disease," said Education Minister Minkailu Bah.
Schools have been closed since the government announced a state of emergency in July in response to an epidemic which has killed 3,500 people in west Africa, more than 600 of them in Sierra Leone.
More than two million of its population of 5.7 million are aged between three and 17, although in reality the secondary school attendance rate is less than 40 percent for both boys and girls.
Bah also admitted that reaching many of the nation's schoolchildren would be difficult in a country where radio ownership is around 25 percent and fewer than two percent have access to a television.
But with no end in sight to the epidemic, which has also engulfed Guinea and Liberia, Sierra Leone's economy and the education of its future workforce are in peril.
"As things now are we cannot expect schools to reopen until early 2015," said Sylvester Meheaux, of the Conference of Principals of Secondary Schools that is helping the government run the classes.
"In the meantime, we are worried some children would end up being dropouts, pregnant and otherwise. These developments are a major concern for us in the educational sector."
Public reaction to the announcement -- which did not include details of how the scheme would be funded -- has been mixed.
"Any means to educate our children rather than leaving them idle is welcome. Otherwise we are going to have a generation of illiterates."
Fatima Sheriff, a single mother from Freetown, said she was worried in particular about the damage the closures of schools was doing to the prospects of young girls.
"For many of them this is the end of their educational dreams as the choice of the going into prostituion and other vices loom," she said.
Manuel Fontaine, the regional director of UN children's fund (UNICEF) which is supporting the initiative, said the radio classes would be focussed on teaching children "life skills" and maintaining their contact with the outside world.
But, he added, it was important that schools reopened as soon as possible, "partly because there is a problem of long-term damage in children who have no education, and because there is a risk that children will drop out of school, of education in general".
Bah, the education minister, said Sierra Leone authorities would "be devising other means (of) accommodating the hard-to-reach areas" without access to radios.
"We are quite aware that not all children will benefit from this method of teaching, but we are doing our best to reach as many children as possible", he said.