They voted to alter it to the Republic of North Macedonia as part of attempts to end a long-running dispute with neighbours Greece. The remaining 39 opposition lawmakers stayed away.
The vote followed intense negotiations between Zaev's center-left coalition and some opposition lawmakers, who had initially agreed to back the agreement but raised last-minute objections.
Opponents to the proposal say they are defending Macedonia's name, identity, and history, as well as the traditions of the Macedonian people, against what they call "the greatest national treachery".
Macedonia's conservative opposition leader has accused the government of securing parliamentary approval for a constitutional amendment changing the country's name by "blackmailing" lawmakers.
Stoltenberg said in a tweet that the name change deal is "an important contribution to a stable and prosperous region".
But in Greece, the upcoming vote on the name-change deal has soured relations between the ruling coalition partners.
European Union foreign policy chief Federica Mogherini said the bloc strongly supports the deal and "remains firmly committed to continue to fully support and accompany (Macedonia) towards its common strategic goal of European Union integration".
During the vote, 81 of the Macedonian parliament's 120 MPs backed the name change, securing the required two-thirds majority to push it through.
"A new historical chapter in our statehood has been written this evening", the Macedonian government said in a statement.
A protest against the name change took place outside the Macedonian Parliament during its Friday session, and a Greek prosecutor on Saturday ordered a probe into alleged threats against pro-deal lawmakers.
Eighty-one lawmakers voted in favor of the constitutional amendments.
Macedonia will soon become a member of North Atlantic Treaty Organisation and then accede to the European Union, Macedonian Prime Minister Zoran Zaev said Saturday.
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.
Mickoski told reporters the move Friday to change the country's name to North Macedonia to appease neighboring Greece was made against the desires of the Macedonian people "and is an act of treason".