This was the second vote on the law after President Gjorge Ivanov failed to sign the decree for its promulgation after the Parliament had initially passed it on June 20.
The opposition did not attend the Parliament session.
Foreign Minister Nikola Dimitrov said in the elaboration that the agreement guarantees the individuality of the Macedonian identity and language.
"The agreement reaffirms and enhances the Macedonian identity as never before. In practice, the agreement will establish the identity and overcome the eternal struggle for language and identity, we will join the EU, including the release of documents in Macedonian language and translated in Macedonian language," said FM Dimitrov.
He said the President is obliged by law to sign the decree after the second Parliament vote.
He referred to the reasons that Ivanov noted when refusing to sign the decree, including the authority of the President to conclude international agreements.
"Since the country's independence, the Parliament has ratified 897 international agreements, of which only five have been concluded by the President", said Dimitrov.
He also mentioned the President's claim that the agreement brings Macedonia into subordinate position to Greece.
"Macedonia was in a subordinate position by the negotiations. The agreement takes us out of that dependency and brings us into a position of independence. It is time to serve the country's interests and show unity," underlined Dimitrov.
Parliament Speaker Talat Xhaferi announced last week that the law could be sent for release to the Official Gazette with only his signature, alongside the Law on the Use of Languages, which President Ivanov has also failed to sign.