People from the EU or US who have been fully vaccinated will not need to isolate when coming to England from an amber list country.
The change will come into force on Monday.
Currently, only people who received their jab in the UK can avoid quarantine when arriving from amber list countries, except France.
The government said the rule change will help to reunite family and friends whose loved ones live abroad.
Transport Secretary Grant Shapps said it will apply to people who have been fully vaccinated with a jab approved by the EU or US – although travellers will still need to take tests before they arrive and on the second day when they land.
It is not yet known whether other UK nations will adopt the same change. Earlier, Scottish First Minister Nicola Sturgeon said talks on travel were taking place between the four nations.
The travel industry has been long pushing for the change in the rules in a bid to make it easier for tourists or those visiting relatives.
The UK’s tourism sector is worth billions of pounds – and travel consultancy boss Paul Charles said the change will “pump vital cash” into the economy.
“It’s especially good news for our airlines who need to fill their seats across the Atlantic,” he said. “The news will encourage millions of extra visitors into the UK at a time when the sector badly needs them.”
But although they will be able to avoid quarantine in England, US citizens are urged not to travel to the UK by their country’s health protection agency, the Centers for Disease Control and Prevention.
And the US border is currently closed to the UK, as well as many other countries, except for US citizens.
The UK and US have set up a taskforce to discuss a travel corridor, although earlier this week the White House said it had no plans to lift Covid-19 travel restrictions for non-Americans.
But Prime Minister Boris Johnson told LBC on Wednesday that “we’re talking to them the whole time”.