British officials noted that the United States had not imposed a similar ban on people from Caribbean nations, which had a higher rate of infection than Britain, or from Argentina, which had a lower percentage of its population vaccinated. About 82 percent of people in Britain above the age of 16 have had two shots.

Britain and several European Union countries allow fully vaccinated people from the United States to travel without quarantining, and officials there were annoyed when the United States did not reciprocate. The European Union has since reversed itself, and issued a recommendation to its members to put more restrictions on American travelers.

“It’s a fantastic boost for business and trade, and great that family and friends on both sides of the pond can be reunited once again,” Mr. Johnson said in a tweet.

The ban, European officials point out, has kept families separated since early 2020, as the coronavirus was erupting across Europe. European countries have weathered a third wave of infections propelled by the Delta variant. But in several countries, including Britain, infection rates have begun to level off and even decline.

The travel ban is one of several sources of tension in the trans-Atlantic relationship. European allies faulted Mr. Biden for not adequately consulting them on the withdrawal from Afghanistan, while France was outraged to lose a lucrative submarine contract with Australia, hours before the United States, Britain and Australia announced an alternative deal to supply nuclear-powered submarines.

But unlike those issues, which are geopolitical and have little day-to-day impact on people, the travel ban has hit Europeans personally. British newspapers played up the fact that the parents of Emma Raducanu, the British woman who won the U.S. Open tennis tournament, could not travel to New York to watch her play.

“Trans-Atlantic travel is massive,” said Steven Freudmann, the chairman of the Institute of Travel and Tourism, an industry lobbying group. “The U.K. travel sector is very keen to open up to the States as soon as possible and is particularly frustrated because we have opened up to fully vaccinated American citizens for some time.”

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