Today's deal makes Turkey Europe's bulwark against its biggest migration crisis since World War II, but comes at a heavy price and amid criticism from rights groups.
"Now unanimous agreement between all EU HoSG (Heads of State or Government) and Turkey's PM on EU-Turkey Statement," EU president Tusk tweeted after talks in Brussels with Ahmet Davutoglu.
Davutoglu smiled and waved on his way into a final meeting with his counterparts to shake hands on the hard-won deal.
"Deal with Turkey approved. All illegal migrants who reach Greece from Turkey as of March 20 will be returned!" Sobotka wrote on Twitter.
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More than 1.2 million migrants have come to Europe since January 2015, and around 4,000 drowned last year while trying trying to reach Europe by sea.
Turkey won an acceleration of its long-stalled bid for EU membership, the doubling of refugee aid to USD 6.8 billion and visa-free travel by June.
In return Turkey agreed to take back all new irregular migrants coming to Greece, the main entry point to Europe.
The deal still faces doubts about how to implement such a huge scheme, not least due to the still often-tense relations between Ankara and Brussels.
President Recep Tayyip Erdogan blasted several EU states for taking only a "handful of refugees" in contrast to the nearly three million Turkey has admitted, most of them fleeing the Syrian war.
"European countries are paying no attention, as if they are dancing in a minefield," he said.
Critics have said the mass expulsion planned under the EU-Turkey deal could infringe international law on the treatment of asylum seekers.