The international travel traffic light system is being simplified with a single red list, as part of an overhaul of the rules from 4 October.
Transport Secretary Grant Shapps also said eight countries would be taken off the red list from Wednesday.
It means people returning from places such as Turkey will no longer have to stay in hotel quarantine.
And PCR tests will no longer be required for fully vaccinated travellers returning to England.
Under the new testing regime, people who have had both jabs will not need to take a pre-departure test before leaving any country not on the red list.
And Mr Shapps said later in October, they would be able to replace the day two PCR test with a cheaper, rapid lateral flow test.
As well as Turkey, Pakistan, the Maldives, Egypt, Sri Lanka, Oman, Bangladesh and Kenya are also being removed from the red list.
The transport secretary said the new travel rules would remain in place “at least until the new year”.
“The purpose is to make it easier to travel without the bureaucracy, without so many tests, and with a greater level of certainty now that we’ve got so many people vaccinated,” he said.
The travel industry said the announcement was a step towards helping tourism recover.
Stewart Wingate, chief executive of Gatwick Airport, said customers can “book with more confidence in the months before Christmas and beyond” and said there was “significant pent-up demand for travel”.
But he said the remaining constraints on travel, such as the need to fill out a passenger locator form, should also be removed.
Bangladesh Foreign minister AK Abdul Momen welcomed the decision.