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 at 04:00 BST 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”.

‘It’s critical’: The people who want the rule change
Isabelle, 56, lives in France and her partner John lives in Kent. Because of the travel rules, the last time she saw him was at Christmas.
As a teacher, she said she could go to England during the summer holidays but would have to quarantine for 10 days.
“What’s the difference between a double-vaccinated French person or Spanish person or British person?” she told the BBC. “There is none. We are using the same vaccines everywhere, so what is the difference?”
France is on the amber list but is currently subject to tougher rules – with quarantine required for UK travellers even if they are fully vaccinated.
Freddie Julius runs tour company Tourist England which puts on trips for overseas visitors. He said around 80% of his customers are from the US and EU and “over the last 18 months we’ve seen almost none”.

He said changing the rules to allow vaccinated tourists to visit without quarantining would be “critical for the revival of the inbound tourism sector”.
But he told the BBC any change needed to be lasting, adding: “The constant easing and tightening of restrictions have made it almost impossible to plan ahead, both for tour companies and tourists.”

Earlier, Labour’s shadow transport secretary Jim McMahon said a decision on opening up to fully vaccinated EU and US travellers should only be made when the scientific advice says it is safe.
“We need to learn to live with Covid,” he said – but that “we don’t know what new variants brought in” could undermine the vaccine rollout.
Labour is calling for an “international vaccine passport” where agreement is reached with countries like America, Canada and the EU, he said.
The aviation industry including British Airways, Virgin Atlantic and Heathrow Airport has been calling for the change after carrying out a 10-day trial of checking the vaccination status of passengers.
The companies said 99% of documents were verified correctly during the trial, which involved about 250 fully-vaccinated participants from the US, the Caribbean and Europe, travelling to Heathrow.