The cash, part of the Home Energy Efficiency Programme for Scotland will be used to improve the energy efficiency of houses by fitting measures such as solid wall, cavity or loft insulation.
Councils will each get a share of £42m from the fund for this work, with the remaining £18m made available to local authorities to develop large scale schemes.
The funding, which is being made available for 2014-15, is part of almost £250m the Scottish Government is investing to tackle fuel poverty and boost energy efficiency over three years, Ms Burgess said.
The housing minister announced the investment on a visit to Annbank in South Ayrshire, where she met residents who have already had their homes improved.
She said: "This £60m investment will help households in fuel poor areas stay warm and reduce their energy bills. In total, the Scottish Government will spend almost a quarter of a billion pounds over a three year period on fuel poverty and energy efficiency.
"Rising energy bills remain a huge concern for this government."