"There is no way back", Zaev told a news conference after speaking with his Greek counterpart Alexis Tsipras by telephone.
The prime minsters of Greece and Macedonia - Alexis Tsipras and Zoran Zaev - had a phone call with each other on Tuesday, and shortly after announced the name change, with Macedonia set to amend its constitution as part of the pact.
The name dispute has poisoned relations between the two countries since Macedonia's independence from Yugoslavia in 1991 and has prevented Macedonia from joining global institutions such as North Atlantic Treaty Organisation and the European Union.
Greece regards "Macedonia" as a term referring only to one of its northern regions and the ancient Kingdom of Macedonia, and insists on the use of another name for its northern neighbor.
The "new" Slavic people calling themselves Macedonians did not help matters when they named the main airport in the capital, Skopje, after Ancient Greek hero Alexander the Great, as well as a key highway running from Skopje to the Greek border.
Skopje took on the name Macedonia in 1991, following its independence, and Greece vetoed its bid to join North Atlantic Treaty Organisation and the European Union over the name dispute.
Zaev said resolving the long-standing issue would open Macedonia's access to North Atlantic Treaty Organisation and the European Union. "The negotiations and the successful proposal for solution became possible after the Government of Zoran Zaev came in to power in Skopje, ending the years of pointless denial of the conservatives in Skopje".
"The former Yugoslav Republic of Macedonia" is no more, stated Zaev, and added that the agreement envisions a confirmation of the Macedonian language without footnotes, and guarantees Macedonian ethnic and cultural identity and nationality.
Because of Greek objections, Macedonia was admitted to the United Nations under a provisional name, the Former Yugoslav Republic of Macedonia.
Mr Tsipras said the deal met the concerns of Greece that a revised name for Macedonia be a "compound" name with a geographical qualifier.
But Greeks seem cool to any deal involving the continued use of the name "Macedonia" by their northern neighbour.
In 1992 more than a million Greeks joined a rally in the northern city of Thessaloniki, once the most important city in ancient Macedonia, to proclaim "Macedonia is Greek".
Both Albania and Macedonia hope to launch full membership negotiations with the European Union.
The deal would also require Macedonia revising its constitution.
European Council President Donald Tusk tweeted his support for the agreement: 'Thanks to you the impossible is becoming possible'.
"This historic agreement is testament to many years of patient diplomacy, and to the willingness of these two leaders to solve a dispute which has affected the region for too long", Stoltenberg said. I believe in the democracy of the internet and want to keep this site and its enriching content free for everyone.
The deal still needs to be approved by the Macedonian and Greek parliaments.
Greek opponents of the deal say it would not go far enough.
The Greek prime minister will now inform the country's president and will later give a televised statement.
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