People receiving Pension Credit will qualify for the warm home discount scheme from the Department for Work and Pensions (DWP).
About 90,100 people who were eligible for the scheme were identified when the DWP cross-checked its records with those of energy suppliers.
Most of the eligible pensioners will automatically have the money taken from their bills between now and January.
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Across the UK, the scheme is expected to result in savings of around £137 million for pensioners.
Pensions Secretary Therese Coffey said: “This Government has actively helped pensioners on low incomes with their energy bills.
“We know how important it is that people keep their homes warm during the cold winter months, which is why I am thrilled that we have used our IT to ensure nearly one million pensioners automatically see their bills reduced.”
UK Government Minister for Scotland Iain Stewart said: “The UK Government’s warm home discount scheme will help protect more than 90,000 pensioners in Scotland on low incomes, ensuring they stay warm as the weather gets colder.
“Looking after our fellow citizens and protecting the vulnerable in our communities is more important than ever as we overcome the coronavirus pandemic.
“I’m delighted this initiative will make a difference to many elderly people in Scotland.”
Those who think they might be eligible for Pension Credit or the warm home discount scheme have been urged to call a free claim line on 0800 99 1234.