The name dispute has poisoned relations between the two countries since Macedonia's independence from Yugoslavia in 1991 and has prevented Macedonia from joining worldwide institutions such as North Atlantic Treaty Organisation and the European Union.
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.
Just to make things confusing, when it became a member of the United Nations in 1993, it had to be given an alternative provisional name of the "Former Yugoslav Republic of Macedonia", which was purely because of the ongoing dispute with Greece.
Macedonian Prime Minister Zoran Zaev addresses the media at the government offices in Skopje, Macedonia on June 12, 2018.
Announcing the agreement reached with neighbouring Greece over the change of name, Macedonian Prime Minister Zoran Zaev said resolving the long-standing issue would open his country's access to North Atlantic Treaty Organisation and the European Union.
"There is no way back", Zaev told a news conference after speaking with his Greek counterpart Alexis Tsipras by telephone.
Macedonian Prime Minister Zoran Zaev said the deal would pave the way for the nation's eventual membership of the European Union and North Atlantic Treaty Organisation.
They also urged the Council to endorse opening EU accession talks with Macedonia, which the European Commission recommended in April.
North Atlantic Treaty Organisation and European Union officials welcomed the breakthrough, which North Atlantic Treaty Organisation secretary general Jens Stoltenberg said would help consolidate regional peace and stability.
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"I now call on both countries to finalise the agreement reached by the two leaders".
In 2001, Greece, the only country in the region with EU, NATO and eurozone membership, expressed support for Skopje, faced by an armed conflict with ethnic Albanian rebels. "And it will help to consolidate peace and stability across the wider Western Balkans".
The name deal must still be ratified by the Macedonian and Greek parliaments and by a Macedonian referendum, expected in September.
Zaev said that the name will be used both domestically and internationally, which should be confirmed by a constitutional amendment.
"The name change will be implemented not only the country's global relations but also domestically", Tsipras said adding that Skopje would need to revise its constitution.
The main opposition party in Macedonia, the conservative VMRO-DPMNE, accused Mr Zaev of "capitulating" to Greece.
The deal would also require Macedonia revising its constitution.
"[Macedonia] can not and will not be able in the future to claim any connection with the ancient Greek civilization of Macedonia".
The move aims to appease Greece, which had opposed the Republic's use of Macedonia, because it sees it as an implication to territorial claims over Greece's northern region of Macedonia.