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 UK 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 the 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.
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.
Responding to the news that fully vaccinated travellers from the EU and US will not have to quarantine on arrival in England, Inverclyde Chamber Chief Executive, George McKay said:
“It is essential that the Scottish Government swiftly update international travel rules to bring them into alignment with those in place in England for vaccinated travellers and we urge the Scottish Government to bring forward a decision on quarantine changes as a matter of urgency for Scotland’s business community.
“Scotland’s business and travel industry will be hugely disadvantaged if these changes aren’t implemented on a four-nation basis and businesses will want to see an early decision made by the Scottish Government to allow them to plan properly ahead of the changes coming into effect on Monday in England.
“Re-opening international travel isn’t only vital for the thousands of people employed directly in Scotland’s travel and tourism industry, but also the wider supply chain, touching on almost every part of Scotland’s economy.
“It’s crucial that the Scottish Government align with the U.K. Government on travel quarantine restrictions to help support business travel, enabling industry and international trade to reboot and begin operating in and out of global markets again.”