Fully vaccinated travellers from the EU and the US will be allowed to avoid quarantine on arrival in England.
However, if people were vaccinated against COVID-19 outside the UK, they still had to quarantine at home for 10 days on return from an amber list country.
Ministers have now approved a change for US and EU passengers from 4am on 2 August ahead of a review on border rules on 31 July.
The UK government said it will now formally recognise American and EU vaccine certificates for people fully vaccinated with a vaccine approved by the FDA (US Food and Drug Administration) or EMA (European Medicines Agency).
As with other amber list countries, travellers will still have to take a pre-departure test and a PCR test the second day after arriving in England.
Sky News looks at how the change could work - and if it will be reciprocated.
How could it work at the UK border?
The trial accepted proof of vaccination through several means, including America's CDC card, US state-level digital certification, and the EU Digital COVID Certificate.
BA customers were able to upload their vaccine status onto the VeriFLY app, developed for BA, American Airlines, Iberia, Aer Lingus and Japan Airlines.
Virgin passengers could upload their status to the FlyReady app, developed with Delta Airlines.
People had to have had their final jab at least 14 days before and the certificate had to include their name, date of birth, dates of vaccination, vaccination type and where it was administered.
Transport Secretary Grant Shapps said the 14-day rule will also apply to those coming from the EU and US under the new plan.
The companies said 99% of documents were verified correctly at the border during the trial, which involved 250 fully vaccinated people from the US, the Caribbean and Europe, travelling to Heathrow.
Two passengers' credentials were rejected - one because they were vaccinated less than 14 days before travel and the other as the name on their passport was different to their vaccine card.
BA chief executive Sean Doyle said the trial provided the government with the evidence it needed to allow fully vaccinated visitors from low-risk countries to come to the UK without self-isolating.
Heathrow boss John Holland-Kaye said there was "no reason to delay rolling out the solution from 31 July".
US vaccine passports
President Joe Biden has ruled out a national vaccine passport app, so it is up to the 50 individual states to decide if they will issue them or not.
More than half, including Florida, Texas, Pennsylvania and Iowa, have banned vaccine certification as they believe it is an overreach of government.
California, Hawaii, Louisiana and New York state have all developed vaccine passport apps.
Some states, such as Maine and New Mexico, have not banned them but do not have an official way of proving a person has had the vaccine, other than their immunisation record card.
The UK has said it will accept certificates from people vaccinated with FDA-approved jabs, which are: Moderna, Pfizer/BioNTech and Johnson & Johnson (Janssen).
EU vaccine passport
The EU Digital COVID Certificate has been rolled out across all 27 member states as well as Switzerland, Iceland, Norway and Liechtenstein.
Citizens can download the certificate or obtain a paper copy at no cost.
Non-EU nationals living in member states can get it, but not British passport holders as the UK is no longer in the EU.
The EU certificate is issued if someone has been vaccinated against COVID-19, but also if someone has had a recent negative PCR test or recently recovered from the virus.
However, UK ministers have indicated they would allow only those who are fully vaccinated.
Only people fully vaccinated with jabs approved by the EMA will be allowed. These are: Moderna, Pfizer/BioNTech, AstraZeneca and Johnson & Johnson (Janssen).
Travel between the US and the UK
It looks unlikely the US will reciprocate the UK opening up to fully vaccinated Americans.
US citizens have been urged not to travel to the UK by the Centers for Disease Control and Prevention (CDC) due to the prevalence of the Delta variant, which is also now widespread in the US.
British travellers, except for US citizens, are not allowed into the US and - despite a US-UK taskforce discussing a travel corridor - the White House said it had no plans to lift travel restrictions for non-Americans.
The EU has encouraged its member states to gradually lift travel restrictions for the UK, but each country has its own rules, with several countries already open to fully vaccinated British passengers.
Britons travelling to major tourist destinations including France, Spain and Greece must prove they have been fully vaccinated, or present a recent negative PCR or antigen test.
Italy requires UK passengers to have a negative COVID test and self-isolate for five days before taking another test.
UK arrivals to Portugal need a recent negative test but the country is only currently accepting the EU digital vaccination certificate, not the NHS pass.