Plans to allow English local authorities to bring forward council tax increases totalling 6% over the next two years to pay for social care are expected to be confirmed by Communities Secretary Sajid Javid.
He is set to announce the proposal, which will add more than £90 to the average bill for a Band D property, on Thursday as part of the local government finance settlement.
Mr Javid is also expected to make the case for longer-term reform of social care funding.
It will come after NHS England boss Simon Stevens said there had been a move from "denial" of a problem in social care funding to "acknowledgement" of an issue he raised in June.
He suggested extra funding could help ease the "most obvious stress" facing the NHS - the number of older people stuck in hospital when they are better off being looked after at home or in a care home.
But Labour leader Jeremy Corbyn has told Theresa May to "get a grip" over the social care funding crisis and criticised her for "passing the buck to local government" in a way which would create a postcode lottery.
At Prime Minister's Questions on Wednesday, he urged the PM to instead scrap plans to cut corporation tax from 20% to 17% in order to plug the spending gap.
Former chancellor George Osborne announced last year that town halls would be permitted to add a 2% "social care precept" onto bills to raise £2 billion a year to help deal with the growing crisis in the sector.
Now authorities will be able to impose the total 6% rise over two years rather than three, meaning a 3% precept would be added to bills in 2017/18 and 2018/19 but 0% in 2019/20.
Chancellor Philip Hammond earlier this week denied reports that he had been blocked by Mrs May from announcing the move in last month's Autumn Statement because of concerns it would hit the "just about managing" families who the Prime Minister has said she wants to help.
Downing Street has said it hopes that a cross-party consensus could be reached on a long-term settlement for social care, hinting at a potential future shake-up of the system.
Council tax on an average Band D property in England was £1,530 in 2016/17, and a 3% rise would increase it by £45.90 next year and the same amount again in 2018/19.
The social care precept comes on top of annual rises in council tax, which are capped at 2% unless the authority wins residents' support for a higher rise in a referendum.
Councils are not obliged to impose the precept, but a survey by the Local Government Chronicle last week found the majority intended to make full use of the 2% then available.
Areas where councils take full advantage of the permitted rises and precepts could now see total bills rise by 10% - or more than £150 - over the next two years, taking the average Band D levy to more than £1,680 a year.
Charities supporting elderly and disabled recipients of social care have welcomed the change as a "step in the right direction", but said it would not fill a black hole in funding estimated by town hall chiefs to reach £2.6 billion by 2020.