"Dear fellow citizens, we have [made] a historic decision..."
According to The Wall Street Journal, many Greek nationalists may still continue to fight the battle over Macedonia's name, and "reject any non-Hellenic claim to the name, even in a composite form".
Greek Prime Minister Alexis Tsipras leaves the Presidential Palace following his meeting with Greek President Prokopis Pavlopoulos (not pictured) in Athens, Greece, June 12, 2018.
Mr Tsipras said the deal met the concerns of Greece that a revised name for Macedonia be a "compound" name with a geographical qualifier.
That challenge will still be a mountain to climb, as Greek Prime Minister Tsipras has not yet secured any support in parliament.
Under the deal between the two prime ministers, the country will now be called The Republic of North Macedonia.
Athens has long objected to its neighbour's constitutional name - the Republic of Macedonia - because it fears it could imply territorial ambitions.
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After splitting from the former Yugoslavia, Macedonia was admitted into the United Nations in 1993 as the former Yugoslav Republic of Macedonia (FYROM).
The name issue has been blocking Skopje's aspirations to join North Atlantic Treaty Organisation and the European Union for years.
"By solving the name question, we are becoming a member of NATO", Zaev added.
In Skopje meanwhile, Macedonian President Gjorge Ivanov said earlier in the day that he remained opposed to a constitutional change that would likely be included in the draft deal, to provide an assurance that the name change was permanent and binding for domestic and worldwide use.
European Council President Donald Tusk congratulated both sides.
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Greece had also vetoed its neighbor's bid to join North Atlantic Treaty Organisation and the EU.
In Greece, Tsipras' conservative rival Kyriakos Mitsotakis also denounced the deal as a "bad agreement".
For Greece, the name Macedonia is part of its own cultural heritage and a source of pride as an ancient province that was the core of Alexander the Great's empire more than 2,000 years ago.
"We must now make good use of the window of opportunity that has been pushed wide open to accompany and consolidate the winds of peace and cooperation in the entire region".
The compromises to resolve the name issue have faced dissent in both countries, threatening to split Greece's governing coalition and provoke a rift between Macedonia's prime minister and president.
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