People arriving in England from more than 50 countries including France, Spain, Germany and Italy will no longer need to quarantine from 10 July, the Department for Transport has confirmed.
A full list of exempt countries posing "a reduced risk" from coronavirus will be published later.
Most travellers to the UK currently have to self-isolate for two weeks.
Scotland and Wales are yet to decide whether to ease travel restrictions and described the changes as "shambolic".
Quarantine regulations also remain in place in Northern Ireland for people arriving from outside the UK and the Republic of Ireland.
England's quarantine restrictions only came into force in early June, in a bid to stop coronavirus entering the country at a time when UK infections were falling.
The new exemptions mean people arriving from selected countries will be able to enter England without needing to self-isolate, unless they have been in or travelled through non-exempt countries in the preceding 14 days.
Transport Secretary Grant Shapps said finalising the list of countries had been delayed - after scrapping the quarantine was announced last week - in the hope that the four UK nations could reach a joint decision.
He said there was "still an opportunity" for Scotland, Wales and Northern Ireland to co-ordinate and therefore make the changes more simple.
But Scottish ministers have complained of being pushed to make decisions too quickly. First Minister Nicola Sturgeon said: "We can't allow ourselves to be dragged along in the wake of another government's - to be quite frank about it - shambolic decision-making process."
First Minister of Wales Mark Drakeford agreed the UK government's approach had been "utterly shambolic".
However, he added it was likely the Welsh government would impose the same measures as in England, provided the chief medical officer for Wales gave approval.
Mr Shapps told the BBC countries on the list would be labelled as either amber or green, in line with a traffic-light system based on their prevalence of coronavirus:
- "Green" countries, such as New Zealand, have "very low" levels of coronavirus and will therefore have restrictions for UK arrivals
- "Amber" countries - including France, Germany, Italy and Spain - will have "reciprocal arrangements" in place, meaning travellers from the UK will not have to quarantine on arrival
- Restrictions will remain in place for "red" countries, including the US
Mr Shapps said Greece would not be on the amber list to begin with, because it was currently not allowing flights from the UK.
Countries that will be either on the green or amber list include some of the UK's overseas territories such as Gibraltar and the Falkland Islands, Mr Shapps said, as well as smaller states such as the Vatican.
Ministers have been under pressure to ease quarantine measures because of the impact on the travel industry.
The Department for Transport said a risk assessment had been conducted considering factors such as the prevalence of the virus, the numbers of new cases and potential trajectory of the disease in each country.
The list of exemptions would be kept "under constant review", so that if the health risks increased, self-isolation measures could be re-introduced, the DfT added.
Mr Shapps said people who were currently quarantining after returning from one of the green or amber countries could stop doing so on 10 July.
Meanwhile, the Foreign Office will set out exemptions for a number of destinations from its current advice against non-essential international travel, which has been in place since 17 March.
All passengers, except those on a small list of exemptions, will still have to give contact information on arrival in the UK and details of where they have been during the previous 14 days.
A spokesman for trade association Airlines UK said changes meant airlines would "be able to re-start services to many key markets in time for peak summer travel".
But he added: "We would encourage rigour and science is applied in all future decisions surrounding our businesses."
The CEO of Gatwick Airport, Stewart Wingate, said it sent "a very clear message that it is now safe to take summer holidays abroad".
He hoped it would be "the start of a turning point" in the aviation industry's recovery from the effects of the pandemic.
The current quarantine policy has been criticised by some Conservative MPs, including former transport minister Theresa Villiers.
She said it had damaged the travel industry without reducing the risk from coronavirus.
Asked about jobs already lost in the hospitality and aviation industries - in part as a result of restrictions on international travel - Mr Shapps said: "The question I suppose everybody would have to ask is where is the right balance between making sure that we put lives first but also protect livelihoods. And this is not an easy balance."
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