Changes look set to be in place on 11 February, the day before half-term departures begin.
Tim Alderslade, Airlines UK chief executive, said: “This is a landmark day for passengers, businesses and UK plc.
“With the all-important half-term week approaching, passengers should now get booking.”
He said the announcement, nearly two years since the initial Covid restrictions were introduced, “brings international travel towards near-normality for the fully vaccinated, and at last into line with hospitality and the domestic economy”.
EasyJet chief executive Johan Lundgren added: "We welcome this news knowing that millions of our customers will also be delighted to see the return of restriction-free travel in the UK. We now look ahead to what we believe will be a strong summer.”
He said testing for travel “should now firmly become a thing of the past”.
“It is clear travel restrictions did not materially slow the spread of Omicron in the UK and so it is important that there are no more knee-jerk reactions to future variants.”
EasyJet planned to return to near 2019 levels of flying this summer, he said.
Virgin Atlantic said the decision was the final step in reintroducing frictionless air travel.
“It restores customer confidence, and demand will be boosted in a critical booking window for the travel industry,” said a spokesperson.
Charlie Cornish, Manchester Airport Group chief executive, said: "This important announcement is excellent news for our sector’s recovery.
“This change will be welcomed by the millions of vaccinated people who are desperate to travel and will now be able to do so – restriction-free – for the first time in more than a year.
"The latest research shows travel restrictions do very little to stop the spread of variants like Omicron. Removing them will ensure the many cultural, social and economic benefits of international travel can be realised without any major impact on public health.”
