"After months of negotiation we've managed to reach a deal that'll solve our longstanding difference over the name of our neighbour," Greek prime minister Alexis Tsipras said on TV.

"There's no way back," Macedonian prime minister Zoran Zaev said.

"By solving the name question, we're becoming a member of Nato," he added.

The dispute had seen Greece veto Macedonia's EU and Nato bids on grounds that its name and constitution contained irredentist claims to a Greek region of the same name.

But the breakthrough is now likely to see EU leaders open accession talks with Macedonia at a summit in June and Nato invite Macedonia to join the military alliance at a summit in July.

The "historic agreement" contributes "to the transformation of the entire region of south-east Europe", the EU enlargement commissioner and foreign affairs chief, Johannes Hahn and Federica Mogherini, said.

"The European Union perspective of the Western Balkans … remains the most powerful stabilising force for the region," they added.

But EU membership remains a decades-long prospect, while Nato, as highlighted by Zaev's comment on "we're becoming a member", offers a more immediate security guarantee.

"I now call on both countries to finalise the agreement reached by the two leaders. This will set Skopje on its path to Nato membership and it will help to consolidate peace and stability across the wider western Balkans," Nato head Jens Stoltenberg said as the news came out.

His comment on the "wider Western Balkans" came amid Western concern that Russia is prepared to use dirty tricks to hold back progress.

The name deal must still be ratified by the Macedonian and Greek parliaments and by a Macedonian referendum, expected in September.

But nationalist forces could try to upset the apple cart in Macedonia, with the opposition VMRO-DPMNE party in Skopje rushing to denounce the deal.

"Today is a hard day for the Republic of Macedonia. We just saw a press conference where a defeat was shown as a fake victory," Hristijan Mickoski, the party chief, said.

Conservative forces in Greece could also cause trouble, with New Democracy, the main opposition party in Athens, urging Tsipras not to sign the "bad agreement".

"Mr. Tsipras does not process the political legitimacy to bind Greece by signing an agreement that does not have the full support of his own government. This has no precedent in Greek political and constitutional history," New Democracy chief Kyriakos Mitsotakis said.

The Former Yugoslav Republic of Macedonia, its official UN designation, will change its name to the Republic of Northern Macedonia, but will be known colloquially as Northern Macedonia under the accord.

It will use its official new name in all internal documents and events and in all international forums.

It will also have to alter its constitution to redact irredentist language before Greece gives its final approval.

"Maybe what has the most historic gravity and value for Greece is that according to this accord ... our northern neighbours don't have, and cannot assert, any link to the ancient Greek culture of Macedonia," Tsipras said on Tuesday, in remarks that might sting a Macedonian nationalist.

"The name change will be implemented not only in the country's international relations but also domestically," Tsipras added, laying down the conditions.

The German chancellor, Angela Merkel, will meet Zaev in Berlin on Wednesday to give her blessing to his efforts to join Europe.

"Sincere congratulations to PM Tsipras and PM Zaev. I am keeping my fingers crossed. Thanks to you the impossible is becoming possible," EU Council president Donald Tusk said.