He said: "It [the education programme] will double enrolment."
The move comes after an earlier initiative that aimed to give free universal primary education.
"It's a pro-poor programme that will help rural communities develop"
acting secondary education commissioner
Many children are prevented from continuing their education beyond primary school because their families are unable to afford the average $130 per year fees.
On average, Ugandans earn about $300 per person per year.
Nsumba-Lyazi said only 150,000 primary school students last year went on to continue their education.
"Without USE [Universal Secondary Education] the dropout rate is about 50 per cent," he said.
Nsumba-Lyazi said the programme would cost an estimated 30 billion Uganda shillings ($17.2m) this year.
About 1,000 government and private secondary schools have been enlisted by the government in order to absorb the new students free of charge.
Uganda, a country of 27 million people, ranks 145th on the United Nations Human Development Index, which measures income, education and life expectancy out of 177 countries.