Sweden has overcome the last remaining hurdle in its quest to become a Nato member as Russia’s full-scale invasion of Ukraine redraws the geopolitical map.

Hungary’s parliament voted on Monday to approve Stockholm’s application to become the 32nd member of the military alliance, which could be formalised as soon as Friday.

“Today is a historic day,” said Ulf Kristersson, Sweden’s prime minister, noting that all Nato’s parliaments have now voted in favour of his country’s accession. “Sweden stands ready to shoulder its responsibility for Euro-Atlantic security.”

The Nato accessions of Sweden and Finland in the past year are one of the biggest geopolitical consequences of Russian President Vladimir Putin’s war in Ukraine.

“Sweden’s membership will make us all stronger and safer,” said Jens Stoltenberg, Nato’s secretary-general, as the Scandinavian nation is ending two centuries of neutrality to seek the security of the alliance’s collective defence pledge.

The entry of the two Nordic countries gives Nato control of almost the entire Baltic Sea aside from the Russian exclave of Kaliningrad. Sweden’s island of Gotland is one of the most crucial locations in the region, and central to any defence of the three Baltic states from any potential Russian attack.

Their accession also transforms Nato’s eastern flank by doubling the alliance’s border with Russia, thanks to Finland’s 1,340km-long eastern frontier.

Stockholm and other European capitals have been stepping up warnings about the possibility of Russia carrying out attacks on other countries beyond Ukraine and testing Nato’s mutual defence clause.

“There could be war in Sweden,” said Carl-Oskar Bohlin, minister for civil defence, last month.

Hungary was the last hurdle in Sweden’s Nato bid after Stockholm overcame long-standing objections from Turkey. Swedish officials became increasingly frustrated with both countries for blocking what could have been the fastest accession process in Nato’s history.

Turkey’s objections centred on Sweden’s historic support for ethnic Kurds, with Ankara demanding it take tougher action against separatist groups. It finally approved Sweden’s Nato bid last month, followed days later by the US agreeing to sell $23bn of F-16 fighter jets to Turkey.

Hungary’s blockade came as more of a surprise to Sweden because ministers in Budapest had repeatedly assured their counterparts in Stockholm that they would not be the last to ratify. Hungary’s government alleged Sweden had denigrated its democratic standards.

“We support the accession,” Hungary’s Prime Minister Viktor Orbán told parliament in Budapest before the vote. “Nato [members] protect each other in the event of an external attack. There is no greater commitment so it is important that . . . we first settle our disputes.”

Although he acknowledged that differences remained, Hungary relented under heavy pressure from the US, Nato and other allies, just as Orbán faced a domestic sex abuse scandal that forced the country’s president to resign.

The Hungarian leader took a swipe at the pressure, telling lawmakers of an “external intervention in the settlement . . . this hindered the resolution”.

Orbán held a meeting in Budapest with Kristersson on Friday as part of the choreography around accepting the Nato application.

Budapest agreed to buy four new Saab Gripen fighter jets from Sweden, bringing its fleet to 18.

“Swedish-Hungarian military co-operation and Sweden’s Nato accession strengthen Hungary’s security,” Orbán said. “So I ask my fellow MPs to [approve] Sweden’s Nato accession.”