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.
The Foreign Office is also changing its advice against all but essential travel to a number of countries from Saturday.
The quarantine restrictions came into force in early June, to try to prevent coronavirus being brought in at a time when infections in the UK were falling.
The new exemptions mean people arriving from selected destinations will be able to enter England without needing to self-isolate, unless they have been in or transited through non-exempt countries in the preceding 14 days.
Transport Secretary Grant Shapps told BBC Breakfast the full list of "50 plus" exempt countries would be published on Friday afternoon.
He said 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.
All 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 there either, Mr Shapps said.
But countries categorised as green, which have "very low" levels of coronavirus, will have restrictions for UK arrivals, he added.
"I take New Zealand as a good example. They do have restrictions when you arrive, but we thought it was right to include them [on the UK's list of exempt countries] because people may want to come here from New Zealand, and that's no particular threat to our hard-won gains that everyone's been going through, staying at home," he said.
The Department for Transport (DfT) added that the devolved administrations would "set out their own approach" to exemption and urged travellers to comply with the relevant rules.
The Scottish government has not yet finalised its decision on easing restrictions on international travel.
The Welsh government is also yet to decide whether it will follow England in relaxing restrictions. In Northern Ireland, quarantine regulations remain in place for travellers arriving from outside the UK and the Republic of Ireland.
Ministers have been under pressure to ease quarantine measures because of the impact on the travel industry.
The DfT said a risk assessment had been conducted by the Joint Biosecurity Centre, in close consultation with Public Health England and the chief medical officer.
It considered factors including the prevalence of the virus, the numbers of new cases and potential trajectory of the disease in that destination, the department said.
The list of exempted countries would be kept "under constant review", so that if the health risks increase, self-isolation measures could be re-introduced, the DfT added.
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.
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Mr Shapps said the move marked "the next step in carefully reopening our great nation".
"The entire nation has worked tirelessly to get to this stage, therefore safety must remain our watch word and we will not hesitate to move quickly to protect ourselves if infection rates rise in countries we are reconnecting with," he said.
All passengers, except those on a small list of exemptions, will still be required to provide contact information on arrival in the UK, including details of countries or territories they have been in or through during the previous 14 days.
A spokesman for trade association Airlines UK said the announcement was "very welcome" and meant airlines would "be able to re-start services to many key markets in time for peak summer travel".
"There's no doubt quarantine has had a devastating impact on our industry and whilst it's welcome the government has removed its blanket ban we would encourage rigour and science is applied in all future decisions surrounding our businesses," he said.
The quarantine policy has been criticised by some Tory MPs, including former transport minister Theresa Villiers.
She said it had damaged the travel industry without reducing the risk from coronavirus.
The announcement comes as the prime minister is due to lead a press conference, ahead of businesses including pubs, restaurants, hairdressers and cinemas reopening in England on Saturday.