The European Parliament and the European Council gave the thumbs up late last night to grant visa-free travel to the two countries on the edge of the bloc, ending an internal EU dispute.
Some EU leaders had felt Brussels was reneging on pledges to ex-Soviet states it has promised to help as they try to move out from Moscow’s shadow.
On Wednesday, the European Council President Donald Tusk warned that the EU was risking its credibility by failing to reward Georgia and Ukraine for painful reforms.
One of the conditions will be governments can reimpose visa requirements quickly, without lawmakers’ approval.
Ukrainian President Petro Poroshenko hailed the move as “encouraging news from Brussels”.
The prospect of easier travel to Western Europe has been used by governments in Kiev and Tbilisi to win popular backing for painful, EU-sponsored reforms.
But EU leaders got cold feet about opening doors to 45 million Ukrainians after the public backlash which followed last year’s refugee crisis in Europe.
Georgia, with only five million citizens, has long been seen as ready for visa liberalisation but has seen its hopes held hostage by EU hesitation over Ukraine, which is bigger, closer and currently stuck in conflict with Russia over the annexation of Crimea.
Facing strong challenges from anti-immigration parties in elections next year, leading powers France and Germany demanded strong controls before any visa deal.
Conservative leader in the EU legislature, Manfred Weber, tweeted after the deal: “Europe is delivering.”