The prime ministers of Macedonia and Greece agreed that it would be known as the "Republic of Northern Macedonia" if the proposal receives the necessary approvals from Macedonia's lawmakers and voters. The new name will be used both domestically and internationally, and Macedonia will amend its constitution as part of the deal.
Ethnic Albanians make up about a quarter of Macedonia's 2.1 million people.
Prime Minister of the Former Yugoslav Republic of Macedonia Zoran Zaev hailed a "historic solution" on Tuesday after Skopje and Athens resolved a longstanding row by agreeing to rename his country the Republic of North Macedonia.
He added that Macedonia "cannot and will not be able in the future to claim any connection with the ancient Greek civilisation of Macedonia".
Athens objected to its neighbor's new name, saying it implied a territorial claim over Greece's province of the same name, which borders the Balkan country.
Last month, at an European Union summit in Bulgaria, Zaev and Greek prime minister Alexis Tsipras discussed a resolution, and the two spoke twice on the phone this week before announcing the deal.
They also urged the Council to endorse opening EU accession talks with Macedonia, which the European Commission recommended in April.
Mr Tsipras said the deal dictates "a clear distinction between Greek Macedonia and our northern neighbours".
The name dispute between Athens and Skopje dates back to 1991, when Macedonia peacefully broke away from Yugoslavia, declaring its independence under the name Republic of Macedonia. "And it will help to consolidate peace and stability across the wider Western Balkans", he added. Tusk said: "Thanks to you the impossible is becoming possible", he said.
"We have a deal", Mr Tsipras said.
"We wholeheartedly congratulate Prime Ministers Alexis Tsipras and Zoran Zaev for their determination and leadership in reaching this historic agreement", said EU foreign affairs chief Federica Mogherini and European Commissioner for Enlargement Negotiations Johannes Hahn in a joint statement. He did not, however, spell out what the name will be.
"Our bid in the compromise is a defined and precise name, the name that is honourable and geographically precise - Republic of Northern Macedonia".
Macedonia had proposed four names to resolve the dispute: Republic of North Macedonia, Republic of Upper Macedonia, Republic of Vardar Macedonia and Republic of Macedonia (Skopje).
In a nutshell, Greek people felt like the name belonged to them because it ties in with the country's heritage and the Macedon Kingdom - the king of which was Alexander the Great, who you'll have heard of. It also has to be ratified by both Macedonian and Greek parliaments.
Defense Minister Panos Kammenos, whose right-wing Independent Greeks party is Tsipras' government partner, said Tuesday he would oppose an agreement in a parliamentary vote.
A resolution of the dispute would see Greece lift objection to Macedonia's accession to North Atlantic Treaty Organisation.