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Fully vaccinated travellers from the EU and the US will not have to quarantine when arriving in England, Scotland and Wales from an amber list country.
Transport Secretary Grant Shapps said the change regarding US and EU arrivals will come into force from 4am on 2 August.
Applicable passengers must have received two jabs with vaccines authorised by the European Medicines Agency (EMA), or in the US with vaccines authorised by the Food and Drug Administration (FDA).
They will still be required to complete a pre-departure test before arriving in England, Scotland and Wales, alongside a PCR test on or before day two after they have landed.
Mr Shapps also announced the resumption of international cruises.
The announcement came after a COVID Operations meeting, which was attended by senior cabinet ministers.
The Department for Transport confirmed separate rules will continue to apply for those arriving from France and that the measures announced on Wednesday "will be kept under review and be guided by the latest data".
They also reiterated that while some restrictions remain in place, travellers "should expect their experience to be different and may face longer wait times than they are used to".
Earlier on Wednesday, deputy leader of the Labour Party Angela Rayner described the then-proposed policy as "reckless".
But Mr Shapps said the rule change is "progress we can all enjoy".
And he also highligted comments from Labour's shadow transport secretary last month, in which Jim McMahon had called for transatlantic travel to be opened up "as soon as it's safe to do so".
"We're helping reunite people living in the US and European countries with their family and friends in the UK," Mr Shapps said in a post on social media.
"From 2nd August at 4am people from these countries will be able to come to the England from an amber country without having to quarantine if they're fully vaxxed.
"The changes will apply to fully vaxxed people with an FDA or EMA vaccine - they'll still need to do the usual pre-departure test before arrival and take a PCR test on day 2 of returning to the England.
"We're also able to confirm the restart of international cruises and flexible testing programmes to help key workers and drive our economic recovery. Whether you're a family or a business, this is progress we can all enjoy."
Mr Shapps added that he expects the US to become more relaxed about allowing Britons to visit "in time".
"We can only set the rules at our end, and that has always been the case. People should always check the rules on the other side," the transport secretary told reporters.
"I've just spoken to my US counterpart today and in the US they still have an executive order which prevents travel from the UK, from Europe, from several other countries to the US.
"So we're saying, 'You can come here, you can come visit, you can come see friends, you can come as a tourist if you've been double vaccinated and follow the rules without quarantine'.
"We can't change that on the other side but we do expect that in time they will release that executive order, which was actually signed by the previous president, and bans inward travel."
Both Scotland and Wales will also allow quarantine-free travel for those fully vaccinated travellers from the EU and the US from amber-list countries, but Northern Ireland has yet to announce if it will also relax the rules.
Health minister Eluned Morgan said the Welsh government "regretted" the removal of quarantine requirements.
But she added the "open border" with England meant it would be "ineffective to introduce separate arrangements for Wales".
"There remain clear public health risks posed by re-opening international travel and removing quarantine restrictions to US and EU fully vaccinated amber arrivals at this time," Ms Morgan said.
"Without self-isolation requirements upon arrival there is a higher risk of importing cases and variants of concern (VoCs) from abroad.
"Vaccines will reduce this risk, but only if they are effective against VoCs. This is why we continue to caution against international travel for non-essential reasons this summer."
But Health Secretary Sajid Javid hailed the quarantine rule change as a "boost to the economy" and said it is "safe from a public health point of view".
"Our vaccination programme is building a wall of defence against this virus so we can safely enjoy our freedoms again, with 7 in 10 adults in the UK now double jabbed," he said.
"By reopening quarantine-free travel for travellers who have been fully vaccinated in European countries and the USA, we're taking another step on the road to normality which will reunite friends and families and give UK businesses a boost."
Currently, those arriving in the UK from amber list locations - which includes the US and much of the EU - must have had both doses of a coronavirus jab as part of the UK's own vaccination programme to avoid the requirement to self-isolate for 10 days.
The government had previously committed to a review of international travel rules by the end of this month.
Ministers said a recent 10-day pilot scheme proved that the COVID vaccination status of travellers from amber list countries could be efficiently and accurately checked away from the border.
The latest quarantine rule change comes as the government was facing mounting pressure from the aviation industry to exempt double-jabbed American and European travellers.
Heathrow CEO John Holland-Kaye described the move as "the right decision".
"The government has made the right decision to safely further reopen international travel. We will now work with colleagues in the industry to boost UK trade, reunite family and friends, and generate billions in new tourist income," he said.
But Labour's Ms Rayner said she was "very concerned" at the prospect of easing quarantine restrictions for more travellers.
"We know that the Delta variant came into this country and delayed the lifting of some of the restrictions and caused infections here," she told Kay Burley on Sky News.
"We need to make sure that we have got a proper data-driven analysis and that we look at an international passport for vaccines.
"And we also know that people who have had the vaccine of course can still get the virus so a testing regime is very important and crucial as well.
"So I am very concerned about the government's announcement via the press this morning."
Under the pilot scheme held by British Airways, Virgin Atlantic and Heathrow Airport, around 250 fully-vaccinated passengers on selected flights from New York, Los Angeles, Jamaica and Athens earlier this month presented their COVID status using paper or digital formats before boarding a plane.
Some 99% of their documents were verified as authentic, with just two passengers' credentials rejected.
In one case there was a discrepancy between the name on their vaccine card and the name on their passport, while another involved someone who had been fully-vaccinated less than 14 days before travel.