The United States, Brazil and China are excluded.
Along with New Zealand on the current Covid-19 'safe list' are Algeria, Australia, Canada, Georgia, Japan, Montenegro, Morocco, Rwanda, Serbia, South Korea, Thailand, Tunisia and Uruguay.
The EU is ready to add China if the Chinese government offers a reciprocal travel deal for EU citizens.
New Zealand Foreign Affairs Minister Winston Peters said though New Zealanders will now be able to travel to the European Union, it did not mean EU residents would be able to come to New Zealand. "We're not changing our settings because of admittedly a very praiseworthy statement from the EU. But we're not going to compromise our country's health."
EU border controls have been lifted for EU citizens travelling inside the bloc.
Rules for UK travellers are covered separately in the Brexit negotiations. UK nationals are still to be treated in the same way as EU citizens until the end of the Brexit transition period on 31 December, so during that time they will be exempt from the temporary travel restriction.
The UK is currently negotiating "air bridges" with several EU member states, so that coronavirus does not totally block summer holidays - the busiest season in Europe for tourism, which employs millions of people.
Last week reports said member states were assessing two different lists. The Politico website said one covered countries with fewer than 16 Covid-19 cases per 100,000 people and the other with up to 20 cases, which would include Canada and Turkey. The New York Times said the list would be revised every two weeks, so the US could be added later.
Earlier this month the European Commission also stressed that reopening borders with non-EU states in the Western Balkans was a priority from 1 July.
However, EU member Croatia announced on Wednesday that travellers from Serbia, Kosovo, Bosnia and North Macedonia would all face 14-day self-isolation, because of an increase in infections.