Ukraine's President Volodymyr Zelensky hailed the decision, made at a summit in Brussels, as "a victory" for his country and Europe.
A spokesperson for Charles Michel, the President of the European Council, said that agreement was unanimous.
Hungary has long opposed talks starting with Kyiv, but withdrew its objection.
Although Prime Minister Viktor Orban did not veto the decision, it was not immediately clear that he supported it.
"This is a victory for Ukraine. A victory for all of Europe. A victory that motivates, inspires and strengthens," Mr Zelensky said in a post on X, formerly known as Twitter.
Ukraine and Moldova applied to join the EU after Russia launched its full-scale invasion of Ukraine in February 2022. They were both given candidate status last June, while Georgia was passed over at the time.
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