"Now unanimous agreement between all EU HoSG, (Heads of State or Government), and Turkey's PM on EU-Turkey Statement," Tusk announced on Twitter, the AFP news Agency reported.
News of the deal had earlier emerged via EU leaders' tweets.
"The Turkey deal was approved," Finnish prime minister, Juha Sipilä tweeted, news agency Reuters reported.
Czech prime mininster Bohuslav Sobotka also used Twitter to announce the deal.
"All illegal migrants who reach Greece from Turkey as of March 20 will be returned!" Sobotka said on the social networking site.
Shortly before these announcements, EU officials said that the 28-member bloc was preparing to deliver a draft of the deal with Turkey to EU leaders. Tusk urged leaders to accept the deal.
"Tusk is ready to table a document for all EU leaders and he recommends its acceptance," an EU source told Swedish Television.
Late on Thursday, Sweden said that it was prepared to assist Greece with ships, aircraft and personnel such as border police, interpreters and case workers to support the implementation of any deal that could see all refugees travelling to Greece from Turkey sent back to Turkey.
"This is a joint task that all 28 member states will have to carry out together so it is only natural that Sweden contributes, too," Swedish PM Stefan Löfven told Swedish Television.
The text of the deal had been hammered out during bilateral meetings between EU officials and Turkey on Thursday night and Friday. The 28 EU leaders reassembled to review the proposal at around 2pm EST.
Under the terms of the proposed agreement, Turkey would take back refugees and immigrants who arrive in Greece, while the EU will accept refugees from Syria, and provide financial support to Turkey.
As part of the deal, Turkish citizens would also enjoy visa-free travel in the EU as early as the summer, and Turkey’s EU membership talks would be given fresh momentum.