Free TV licences for up to 3.7m pensioners are being scrapped, the BBC has announced.
Under the new rules, only low-income households where one person receives the pension credit benefit will still be eligible for a free licence.
In 2015, the government announced the BBC would take over the cost of providing free licences for over-75s by 2020 as part of the fee settlement.
But that would have cost £745m, a fifth of the BBC's budget, by 2021/22.
The new scheme will cost the BBC around £250 million by 2021/22 depending on the take-up.
Funding free TV licences for all over-75s would have resulted in "unprecedented closures", the BBC said.
The broadcaster said that BBC Two, BBC Four, the BBC News Channel, the BBC Scotland channel, Radio 5live, and a number of local radio stations would all have been at risk.
The BBC said "fairness" was at the heart of the ruling, which comes into force in June 2020.
It follows a consultation with 190,000 people, of whom 52% were in favour of reforming or abolishing free licences.
According to the BBC, around 900,000 households are claiming pension credit, which is a government benefit paid weekly to pensioners on low incomes.
The number of households which could be eligible to apply for pension credit could number 1.5 million by 2020.
BBC chairman Sir David Clementi said it had been a "very difficult decision" but this was the "the fairest and best outcome".
But Prime Minister Theresa May said she was "very disappointed" with the BBC's decision.
A government spokesperson said: "We've been clear that we want and expect the BBC to continue this concession.
"People across the country value television as a way to stay connected, and we want the BBC to look at further ways to support older people."
The spokesman said taxpayers want to see the BBC using licence fee income better, including "showing restraint on salaries for senior staff".
But Labour's deputy leader Tom Watson said the government bore responsibility for the "outrage" of charging over-75s the licence fee, having promised to maintain free licences in the Conservative Party's 2017 manifesto.
"Millions of elderly and isolated people will lose because of this announcement," he said.
Analysis by David Sillito, media correspondent
Free licences were given to the over-75s as part of a Labour government programme to reduce pensioner poverty. Fifteen years later that government funding was cut by the Conservatives.
Ever since then, the BBC has been pondering if it can afford to take on the bill. It's a cost that's rising every year as the number of pensioners continues to grow. In 2020 it's estimated there will be around 4.6 million households with at least one pensioner.
This then is a compromise; around a third of the cost will be borne by the BBC and two thirds passed on to 'wealthier' pensioners. The elderly are by far the biggest consumers of the BBC's output, the average age of BBC TV's audience is now over 62, the question is how far younger licence fee payers should subsidise these older viewers.
As consumption of traditional TV by younger viewers continues to drop there could well be questions about why they are being expected to pay for a service that the heaviest users get for free.
One in four over-65s say the TV is their main form of companionship, according to Caroline Abrahams, charity director of Age UK.
She said: "Make no mistake, if this scheme goes ahead we are going to see sick and disabled people in their eighties and nineties who are completely dependent on their cherished TV for companionship and news forced to give it up."
Elderly people are likely to feel "enormous anxiety and distress, and some anger too", she said, adding: "But in the end this is the government's fault, not the BBC's."
The National Pensioners Convention said the BBC "has done the government's dirty work for it".
But the Intergenerational Foundation, a charity which supports the interests of younger members of society, said it was fairer to make wealthier pensioners pay.
"There is simply no reason why retired judges, lawyers, bankers and doctors should receive a free TV licence when younger generations are struggling financially," the charity said.
£154.50Annual cost for colour TV
£745mEstimated cost to the BBC of current scheme by 2021/22
£250mEstimated cost of new scheme depending on take-up
190,000people consulted on the change
52%in favour of reforming or abolishing free licence scheme
Free licences were first introduced by the Labour government in 2000 at the same time as half-price licences for the visually impaired.
In 2015, the Conservative government announced the BBC would take over the cost of providing free licences for over-75s by 2020 as part of the fee settlement.
Following the announcement, TV Licensing is advising customers receiving a free licence that they need not take any immediate action.
Over the course of the next month, TV Licensing will be writing to everyone who currently has a free over-75 licence to let them know about the new scheme and make clear that they will remain fully covered until 31 May 2020.
A free telephone information line will also be launched this month where older customers and their relatives can access information on the new policy and a new "pay as you go" payment scheme will be launched from June 2020 which will let people spread the cost of the licence in fortnightly or monthly payments.
The BBC's consultation was announced in November last year. Nearly half of respondents (48%) said they were in favour of continuing concessions to over-75s.
Reforming the current rules was backed by 37% of respondents, with 15% in favour of scrapping concessions of over-75s.