The countries struck the deal in June, but FYROM will start using the new name only after the parliament in Athens also ratifies the agreement.
Macedonian politicians voted on Friday (Jan 11) to change the country's name to "Republic of North Macedonia", settling a decades-long row with Greece and paving the way for NATO and European Union membership.
Representatives of the conservative opposition VMRO-DPMNE boycotted the vote.
The change is the result of a dispute between Macedonia and Greece over history and national identity that has lasted 27 years.
But the Macedonian constitution stipulates that as the measure was passed by a two-thirds majority, the president has no choice but to sign it into law.
Stoltenberg said in a tweet that the name change deal is "an important contribution to a stable and prosperous region". Mickoski told reporters the constitutional changes were approved against the desires of the Macedonian people and described the vote as "an act of treason".
"A better deal could not be reached, and without an agreement with Greece there will be no North Atlantic Treaty Organisation and European Union (membership)", Zaev said.
She said the European Union strongly supports the deal and will "fully support" Macedonia's goal of joining the EU.
Separately, Greek Prime Minister Alexis Tsipras previously stated that they were planning to take this agreement to the Greek Parliament in January.
The vote came after three days of negotiations between Zaev and lawmakers that opposed the change.
For the deal to come into effect, Greece's parliament must now convene in coming weeks to ratify it.
- This item corrects the number of opposition lawmakers staying away to 39.
Parliamentary speaker Talad Xhaferi said 81 MPs had voted in favour of the name change in the 120-seat chamber, securing the required two-thirds majority.
Adding his congratulations late Friday, was Matthew Nimetz, the U.N. Secretary-General's personal envoy on the name dispute since 1999, who said that the agreement is a move towards 'a firmer basis for peace and security in the Balkans'.
"A new historical chapter in our statehood has been written this evening", the Macedonian government said in a statement.
Greece is bound by terms of the deal to stop blocking Macedonia from NATOand other global groups and to allow it to start European Union accession talks as part of the deal.