Greek Prime Minister Alexis Tsipras on Friday congratulated Macedonia counterpart Zoran Zaev after deputies in Skopje voted to change the country's name to the Republic of North Macedonia, his office said.
"The prime minister congratulated Mr Zaev on the successful conclusion of the process to revise the constitution of the former Yugoslav republic of Macedonia," Tsipras' office said in a statement.
Revising the constitution to change the country's name to the "Republic of North Macedonia" was part on an agreement signed by Tsipras and Zaev in June.
Tsipras said earlier this week that Greece's parliament would also be asked to ratify the Prespes agreement by the end of the month.
"Within ten days, in any case as soon as the (Macedonia parliamentary vote) result is notified to us and if we see that everything is in order, we will vote (to approve) the Prespes Agreement," he told Open TV.
The deal was signed in the border Prespes region, after months of talks with Skopje.
Tsipras added that a separate vote on a protocol to enable Macedonia to join NATO would be held "not long afterwards".
The vote in Athens threatens to destabilise Tsipras' ruling coalition, as the junior party in government, the nationalist Independent Greeks (ANEL) party, strongly opposes the Prespes agreement.
ANEL leader Panos Kammenos, who is Tsipras' defence minister, has threatened to pull out of the government when the deal comes to a vote in Athens.
The main opposition conservative New Democracy party also rejects the agreement, but Tsipras can rely on lawmakers from the small pro-EU To Potami party to get it approved.
Greece has previously blocked its neighbour's accession to NATO and the European Union ever since Macedonia broke away from the former Yugoslavia in 1991.
For the Greeks, Macedonia is the name of a history-rich northern province that was the cradle of Alexander the Great's ancient empire.
The previous government in Skopje had angered Athens by staking a claim to Alexander's heritage, a process reversed by Zaev.