Georgia, along with much larger Ukraine, has been urging the EU to grant visa-free travel so as to show its citizens that close ties with Europe can deliver concrete benefits.
EU Migration Commissioner Dimitris Avramopoulos said the decision marked "a historic day for Georgia and its citizens."
"Today's adoption recognises 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.
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.
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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.