The list includes Algeria, Australia, Canada, Georgia, Japan, Montenegro, Morocco, New Zealand, Rwanda, Serbia, South Korea, Thailand, Tunisia and Uruguay, it stated.
The EU is also opening borders to China soon.
The survey, commissioned by the European Council on Foreign Relations, a pan-European think tank, interviewed 11,000 people from nine European countries from the last week of April this year to early May, reported CNBC.
The agreement is non-binding, but countries allowing in travelers from non-listed external countries risk having their European Union peers again closing the borders and not letting the citizens of non-abiding countries enter.
The E.U.'s 27 members have been drawing up a list of countries whose virus levels are deemed low enough to allow people from those places to travel into the bloc, which has been mostly sealed off since March. However, most Americans have been refused entry for at least two weeks owing to the soaring coronavirus infections in the U.S., reports said.
More than 125,000 people in the US have died from the coronavirus since the pandemic began, according to an NBC News tally.
The criteria used to approve countries for travel include if the number of new cases over a 14-day period was close to or below the EU's average per 100,000 people. As many as 54 countries had been reviewed, but only 15 were included in the final list.
The gradual lifting requires coordination between 30 countries, including four European Union countries who have yet to join the Schengen area - namely Bulgaria, Romania, Croatia and Southern Cyprus - and four non-EU members of the borderless zone (Norway, Lichtenstein, Switzerland, Iceland).
The restrictions also apply to the tiny nations of Andorra, Monaco, San Marino and the Vatican.