Under the controversial deal, which came into force at midnight, all migrants landing on the Greek islands face being sent back to Turkey.
And in a grim start to an agreement designed to stop people from making a journey fraught with danger, two little girls were found drowned and two Syrian refugees died of heart attacks after the crossing.
Nine more died and hundreds were rescued off Libya, the Red Crescent said, as fears grow that the shutdown of the Greek route could encourage more people to attempt the even riskier Mediterranean crossing to Italy.
Officials said it would take time to start sending people back, as Greece awaits thousands of European staff needed to take on the daunting task of mass repatriation.
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The SOMP agency coordinating Athens' response to the crisis insisted however that those arriving from today faced certain return to Turkey.
"They will not be able to leave the islands, and we are awaiting the arrival of international experts who will launch procedures for them to be sent back," the agency said.
France and Germany have offered to send up to 600 police and asylum experts, while Romania said today that it would send 70.
Under the deal, for every Syrian among those sent back from Greece to Turkey, the EU will resettle one Syrian from the Turkish refugee camps where nearly three million people are living after fleeing their country's brutal civil war.
The EU will also speed up talks on Ankara's bid to join the 28-nation bloc, double refugee aid to six billion euros (USD 6.8 billion), and give visa-free travel to Turks in Europe's Schengen passport-free zone by June.
But Amnesty International has called the deal a "historic blow to human rights," and yesterday thousands of people marched in European cities including London, Athens, Barcelona and Amsterdam in protest.