The new Chancellor, Philip Hammond, has announced the scheme will be closed at the end of the year, though he insisted it was always due to finish then.
It is the latest in a series of major policy U-turns since Mr Cameron left Downing Street in July and Mrs May sacked Mr Osborne as Chancellor in her first act as Prime Minister.
The U-turns include:
:: Ending the ban on new grammar schools
:: Making immigration sustainable rather than cutting by tens of thousands
:: Watering down the childhood obesity strategy
:: Threatening to cancel the Hinkley Point nuclear power station
:: Changing the priorities of Mr Osborne's "Northern Powerhouse"
Mr Hammond announced the ending of the Help to Buy guarantee scheme in a letter to the Bank of England governor Mark Carney.
He said the scheme was "introduced with a specific purpose that has now been successfully achieved" and that it would close at the end of the year.
It meant that buyers only needed to find a deposit of 5% of the value of their home, with a mortgage covering the remaining 95%.
As its closure was announced, the Treasury published new figures revealing that more than 86,000 households have been supported by the initiative.
But the Government says it is no longer needed as confidence has returned to the market, with more private lenders offering 90% to 95% mortgages.
Across all of the Government's Help to Buy schemes, a total of 185,000 homes were bought, including more than 150,000 properties for first time buyers.
In his letter, Mr Hammond said the Bank of England's Financial Policy Committee has assessed that the move to drop the scheme is "unlikely, in current market conditions, to affect significantly the provision of finance" to Britons hunting for a mortgage.
He added: "It is important to note that the end of this particular scheme does not diminish in any way the Government's commitment to supporting those looking to get on the housing ladder."
Ministers stressed there are still schemes to help Britons looking to buy their first home, including Help to Buy ISAs and shared ownership.
Paul Smee, of the Council of Mortgage Lenders, said: "Help to Buy continues to give a welcome leg-up to many creditworthy buyers who may not otherwise have been able to get a foothold on the property ladder.
"The scheme has helped buyers right across the country, including a high proportion of younger borrowers and first-time buyers."
But Sam Dumitriu, of the Adam Smith Institute, said Mr Hammond was right to dump Mr Osborne's "misguided mortgage guarantee scheme".
He added: "Britain's housing crisis is the result of supply being unable to meet rising demand.
"Help to Buy only served to make this problem worse, pushing up prices through cheap credit, while doing nothing to address the underlying housing shortage."