The support equates to 80% of workers' salaries up to £2,500 a month and will be available throughout the UK during the period.
It will be reviewed in January to determine whether employers should contribute more.
Sunak told the House of Commons: "We can announce today that the furlough scheme will not be extended for one month, it will be extended until the end of March.
"The Government will continue to help pay people's wages up to 80% of the normal amount. All employers will have to pay for hours not worked is the cost of employer NICs and pension contributions.
"We will review the policy in January to decide whether economic circumstances are improving enough to ask employers to contribute more."
Sunak also announced additional support for the self-employed, with the next income support grant for November to January increasing to 80% of average profits up to £7,500.
The Scottish and Welsh governments earlier argued the scheme should be on offer if they also enter full national lockdowns.
Sunak told the Commons "upfront guaranteed funding" for the devolved administrations will increase by £2 billion.
He added: "I also want to reassure the people of Scotland, Wales and Northern Ireland. The furlough scheme was designed and delivered by the Government of the United Kingdom on behalf of all the people of the United Kingdom, wherever they live.
"That has been the case since March, it is the case now and will remain the case until next March.
"It is a demonstration of the strength of the Union and an undeniable truth of this crisis we have only been able to provide this level of economic support because we are a United Kingdom."
The Bank of England has already announced it will pump a further £150 billion into the economy.
Andrew Bailey, the central bank’s governor, said the decision was made after the “dramatic impact” of the impact of the coronavirus.