The Energy Efficiency Standard for Social Housing (EESSH) aims to help reduce energy consumption and fuel poverty among householders in Scotland.
The Scottish Government said raising energy efficiency ratings from the current Scottish Housing Quality Standard will save an estimated £130 million in fuel costs each year.
The move is also expected to reduce annual carbon emissions from housing.
Ms Burgess announced the details on a visit to a housing association development in Linwood, Renfrewshire.
She said: "Achieving the new Energy Efficiency Standard for Social Housing is expected to save social housing tenants £210 annually on average, helping to reduce the impact of rising energy prices.
"In addition to helping to reduce fuel poverty, the EESSH will also help reduce greenhouse gas emissions, and contribute towards ambitious climate change targets.
"Scotland is outperforming the UK in the delivery of home energy efficiency measures that save tenants money, and the introduction of this standard will help enhance our performance for many of the poorest households.
"Nonetheless, rising energy prices remain a huge concern for this government, and we will spend almost a quarter of a billion pounds over three years on fuel poverty and energy efficiency.
"While we have managed to help thousands of households to have warmer, more energy efficient homes, with independence we would be able to change the way energy efficiency is funded to help even more people."