Athens, which has a northern region also called Macedonia bordering on the ex-Yugoslav republic, objected to the name, demanding it be changed.
'There is an agreement.
Zaev said that there will be "a referendum where the citizens will decide, because they are the ones who chose us and are still supportive of our governance".
He added that Macedonia "cannot and will not be able in the future to claim any connection with the ancient Greek civilisation of Macedonia".
Macedonia proclaimed its independence from Yugoslavia in 1991 but its worldwide recognition was immediately blocked by Greece because of the name. "I'm happy because we have a good deal which covers all the preconditions set by the Greek side", Tsipras said, according to Radio Free Europe/Radio Liberty.
European Union and North Atlantic Treaty Organisation officials have welcomed a deal between Greece and Macedonia resolving a decades-long dispute over the Balkan country's name.
European Council President Donald Tusk tweeted his support for the agreement: 'Thanks to you the impossible is becoming possible'. "I am keeping my fingers crossed". The Greek parliament will also have to agree to the proposal.
'It's clear that (Macedonia) bears no relation to the ancient (Macedonian) culture. and that their language belongs to the Slavic language, ' he said.
Basically, way back in 1991 the two countries fell out when Macedonia gained independence from Yugoslavia.
He is close to a nationalist party which was defeated by Zaev in elections a year ago. NATO Secretary-General Jens Stoltenberg's statement refers to "the agreement between Athens and Skopje" rather than naming the countries.
The announcement came after telephone talks with Greek counterpart, Alexis Tsipras, on Tuesday.
Greece's parliament will be called to ratify the agreement after Macedonian lawmakers approve it, provided that Skopje fulfils preliminary European Union and North Atlantic Treaty Organisation requirements to begin membership talks, Kotzias said.
Skopje hopes to secure a date to begin accession talks at an European Union summit in late June, and an invitation to join North Atlantic Treaty Organisation in mid-July.
Stoltenberg said: "This will set Skopje on its path to North Atlantic Treaty Organisation membership. And it will help to consolidate peace and stability across the wider Western Balkans".
The EU's enlargement commissioner Johannes Hahn and foreign policy chief Federica Mogherini responded with an enthusiastic welcome for the agreement.
Greece had long demanded that Macedonia change or modify its name to avoid any claim to the territory and ancient heritage of Greece's northern region of Macedonia - birthplace of ancient warrior king Alexander the Great.