By Francesca Gillett & George Bowden
People who have been fully vaccinated in the EU or US 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 jabs in the UK can avoid quarantine when arriving from amber list countries, except France.
The government said the rule change would help to reunite family and friends whose loved ones live abroad.
Transport Secretary Grant Shapps said it would apply to people who have been fully vaccinated with a jab approved by the EU or US.
Travellers will still need to take PCR Covid tests pre-departure and on the second day after they arrive.
Tougher rules will continue to be in place for France, which is on the amber list but still requires travellers to quarantine when they return, even if they are fully vaccinated.
Mr Shapps said this advice would reviewed at "the end of next week" as part of the rolling assessment of travel rules.
As well as reopening to the EU and the US, international cruises will also be allowed to restart from England.
It is not yet known whether other UK nations will adopt the same changes. Earlier, Scottish First Minister Nicola Sturgeon said talks on travel were taking place between the four nations.
Welsh First Minister Mark Drakeford said Wales would reflect the changes, subject to more information about how approved jabs would be verified.
At-a-glance: latest changes
The travel industry has long been pushing for this change in a bid to make it easier for tourists or expats to visit.
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".
Family, friends - and tourism
For 70-year-old Patricia Duncan in Spain, the changes will mean she can travel to England and be on hand to support her daughter ahead of an operation - without needing to isolate.
"I have another friend with mental health issues who is desperate for me to visit," she says.
"Normally I travel three or four times a year to see my family and friends, and it's been a long time. So I'm very glad that is happening."
But Fiona Clarke in Portugal says the cost of Covid testing is still a barrier for her to visit family in Brighton.
"I think we'll look very carefully, we'll wait and see what happens with the testing," she says.
Freddie Julius runs tour company Tourist England which puts on trips for overseas visitors. He said around 80% of his customers were 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."
Labour deputy leader Angela Rayner said she had "real concerns" over the plan - saying: "Each individual US state does things differently," she said. "They don't have a National Health Service that has a vaccine programme like we do with the certifications.
"So we're really concerned about making sure that new variants do not come into the UK and that we do have a system that identifies where we have variants of Covid where infection is and we're able to isolate it."
British Airways welcomed the latest changes, but called for the government to go further by adding the US to the green list after the recent decline in daily cases recorded in the UK and the rise in those protected by vaccines.
Several airlines said 99% of vaccination documents were verified correctly during a recent trial, which involved about 250 fully-vaccinated participants from the US, the Caribbean and Europe, travelling to Heathrow.