ATHENS—Greeks overwhelmingly voted against their international creditors’ conditions for further bailout aid, in a result that could deepen the rift between Greece and the rest of Europe and push the country closer to bankruptcy and an exit from the euro.

More than 61% of Greeks voted “no” in Sunday’s referendum on austerity measures and other overhauls that European and International Monetary Fund officials had demanded in recent talks—an outcome that spurred popular celebrations into the night across downtown Athens and...