"I have achieved what I wanted and I think it is right to end it at this point," the 31-year-old team captain told a news conference on Tuesday. He is due to return to the United States on Thursday, where he plays for the NBA's Miami Heat.
The announcement comes a day after around 20,000 people welcomed the triumphant team in the centre of Slovenia's capital Ljubljana, following the stunning 93-85 victory over Serbia in the final in Istanbul.
The game, in which Dragic scored 35 points on the way to being named the tournament's Most Valuable Player (MVP), was the most watched sports TV event in Slovenia's history, according to local broadcaster Pro Plus.
The win is the country's first major basketball triumph, and goes some way to make up for the overtime loss to Serbia in the semi-finals of the 2009 Eurobasket.
Both Slovenia and Serbia emerged from the breakup of the former Yugoslavia, with Slovenia being the first to declare independence in 1991.
On Monday, Slovenia's President Borut Pahor awarded the team one of the highest state honours, a Golden Order for Merits for their achievement.
(Reporting By Marja Novak; Editing by Christian Radnedge)
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