The move would end more than two centuries of military nonalignment and instantly turn Sweden and Finland - which share a 830-mile border with Russia - from neutral nations to hostile and potential targets for Moscow.
Swedish Prime Minister Magdalena Andersson said Sweden would hand in its Nato application jointly with Finland.
Ms Andersson warned that the Nordic country would be in a “vulnerable position” during the application period and urged her fellow citizens to brace themselves for the Russian response.
“Russia has said that that it will take countermeasures if we join Nato,” she said.
“We cannot rule out that Sweden will be exposed to, for instance, disinformation and attempts to intimidate and divide us.”
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Sweden's announcement came a day after the country's governing Social Democratic party endorsed a plan for Sweden to join the trans-Atlantic alliance, while Finland's government announced that it would also seek to join it.
Moscow has repeatedly warned Finland and Sweden of repercussions should they pursue Nato membership - but President Vladimir Putin on Monday seemed to downplay the significance of their move.
Speaking to a Russian-led military alliance of six ex-Soviet states, Putin said Moscow “does not have a problem” with Sweden or Finland applying for Nato membership, but that “the expansion of military infrastructure onto this territory will, of course, give rise to our reaction in response."
Flanked by opposition leader Ulf Kristersson, Ms Andersson said her government also was preparing a bill that would allow Sweden to receive military assistance from other nations in case of an attack.
“The Russian leadership thought they could bully Ukraine and deny them and other countries self-determination," Mr Kristersson said.
“They thought they could scare Sweden and Finland and drive a wedge between us and our neighbours and allies. They were wrong.”
Ms Andersson said Sweden would make clear that it doesn't want nuclear weapons or permanent Nato bases on its soil - similar conditions as neighbouring Norway and Denmark insisted on when the alliance was formed after World War Two.
What could stop them from joining?
Countries can only join Nato if all current members agree.
The announcement on Monday drew strong objections from Turkey - a key Nato member who declared the two nations should not be allowed to join because they have been too lax in taking action against Kurdish militants.
Turkish President Recep Tayyip Erdogan on Monday ratcheted up his objection to Sweden and Finland joining, accusing the countries of failing to take a “clear” stance against Kurdish militants and other groups that his country considers terrorists, and of imposing military sanctions on Turkey.
Erdogan also accused the two countries of refusing to extradite “terrorists” wanted by his country.
“Neither country has an open, clear stance against terrorist organisations,” Mr Erdogan said.
“During this process, we cannot say ‘yes’ to those who impose sanctions on Turkey, on joining Nato, which is a security organisation.”
Swedish Defence Minister Peter Hultqvist told public broadcaster SVT that a Swedish delegation would be sent to the Turkish city of Ankara to discuss the issue.
The Swedish and Finnish governments swiftly initiated discussions across political parties about Nato membership and reached out to the US, the UK, Germany and other member countries for their support.
In a joint statement, Nordic Nato members Norway, Denmark and Iceland said they were ready to assist Finland and Sweden "with all necessary means” during the application process.
Why have Sweden and Finland decided to join Nato now?
Sweden, once a regional military power, has avoided military alliances since the end of the Napoleonic Wars.
Like Finland, it remained neutral throughout the Cold War, but formed closer relations with NATO after the 1991 Soviet collapse.
They no longer see themselves as neutral after joining the European Union in 1995, but have remained nonaligned militarily until now.
After being firmly against Nato membership for decades, public opinion in both countries shifted following Russia's February 24 invasion of Ukraine, with record levels of support for joining the alliance.