Priority will be given to those who have not previously entered or tried to enter Europe, with the EU limiting places for up to 72,000 people.
These will be shared out among member states under its existing quota scheme.
After less than an hour of talks both the prime ministers of Finland and the Czech Republic posted on Twitter from inside a Brussels summit that the 28 EU member states had approved the deal with Turkey.
The plans were drawn up by European Council president Donald Tusk and Turkish prime minister Ahmet Davutoglu.
The cut-off date is March 20 – that is on Sunday. All migrants arriving after that cut-off date will be returned after individual assessment.
He added: “The cut-off date is March 20 – that is on Sunday. All migrants arriving after that cut-off date will be returned after individual assessment.”
The spokesman said the new arrangements would come into force at the end of Sunday, so the first migrants facing return would be those crossing the Aegean Sea to the Greek islands on Monday morning.
A senior Turkish official said it will begin re-accepting migrants from April 4.
Under a draft of the agreement, the deal will also see Turkey take greater action to prevent new migrant routes to Europe opening up, while the EU will speed up the release of €3billion already promised to help fund refugee projects in Turkey and also pledge a further €3billion in aid before the end of 2018.
As well as fast-tracking Turkey’s bid for EU membership, the country’s 77million citizens will also be considered for visa-free travel to Europe’s Schengen Zone as early as June, under the terms of the draft deal.
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