EU Migration Commissioner Dimitris Avramopoulos said the decision marked "a historic day for Georgia and its citizens."
"Today's adoption recognizes the tremendous efforts undertaken by the Georgian authorities and the Georgian people to carry out far-reaching and difficult reforms," Avramopoulos said, according to a statement of his remarks in Tblisi, the Georgian capital.
Georgia had long been seeking the waiver and Commissioner Avramopoulos called it "a historic day for Georgia and its citizens."
"These reforms also bring Georgia closer to EU standards, facilitating cooperation with the European Union and bringing the country a step forward on its European path," he added.
Under the accord, which now requires formal signature by the 28 member states and the European Parliament, Georgian citizens will be able to travel visa-free for 90 days in the EU during any 180-day period.
The accord does not apply to the United Kingdom or Ireland.
The original plan caused some concern that Georgians might abuse the system to come and stay illegally in a European Union still grappling with the aftermath of the 2015 migrant crisis.
In December, member states decided to allow visa requirements to be reintroduced at short notice if there was an upsurge in arrivals.
Like Georgia, Ukraine sees visa-free travel to the EU as part of a geopolitical tussle with Russia over the ex-Soviet states' Western aspirations, which Moscow opposes.
The issue of fostering closer ties with the EU was at the heart of mass street protests in Kiev that toppled a Moscow-allied president there in early 2014.
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