The decision is widely seen as a historic step for Bosnia, raising hopes that the country could move beyond instability marked by ethnic rivalries and secession threats, nearly three decades after the end of a devastating war.
"Today is one of the best days in the history of Bosnia and Herzegovina," Foreign Minister Elvedin Konakovic told N1 TV, while Sarajevo's main street was decorated with hundreds of EU flags.
EU leaders agreed that the bloc would take the next step toward membership talks - the adoption of a negotiating framework - as soon as Bosnia took "all relevant steps" recommended by the European Commission.