The European Union (EU) will continue to ban travellers from the United States, Russia, Brazil and most other countries beyond 1 July, according to EU diplomatic sources.
Only 14 countries made it onto the list of states whose nationals will be allowed into the bloc.
Chinese citizens will be allowed in principle - but only once China lifts its ban on EU citizens.
The European Council on Monday began the formal procedure to officially adopt the agreement, according to EU diplomats.
An official announcement is expected on Tuesday.
The list of countries
The countries that will see restrictions lifted as of July 1 are Algeria, Australia, Georgia, Japan, Canada, Morocco, Montenegro, New Zealand, Rwanda, Serbia, South Korea, Thailand, Tunisia and Uruguay.
The agreement comes three months after the EU - plus Switzerland, Norway, Iceland and Liechtenstein - closed its external borders to all non-essential travel due to the coronavirus pandemic. An exception is Ireland, which did not implement the EU's non-binding external travel ban because of its travel agreement with non-EU member Britain.
Under the ongoing travel restrictions, entry to EU countries is only granted in exceptions, such as for long-term EU residents, family members of EU nationals and diplomats.
Monday's agreement follows weeks of intense discussions between EU member states about which countries the group should open its borders to and which ones to ban.
Some countries had been reluctant to continue banning US citizens while opening to China as this could carry political implications, such as risking to anger close ally Washington.
Epidemiological factors
The rules are mainly based on epidemiological factors as suggested by the European Commission on Thursday last week.
The list will be re-evaluated every two weeks. For restrictions to be lifted, the number of new infections over the past two weeks should be "close to or under" 16 per 100,000 people. This is the EU average.
The decision on which countries to ease the restrictions for will also take into account how governments responded to the coronavirus pandemic.
According to the official EU health agency ECDC, the US registered more than 120 new cases per 100,000 inhabitants over the past two weeks.
