Both countries submitted their applications this week to be part of the defence alliance, a drastic shift in European geopolitics.
The move by the two Nordic nations has been opposed by Nato ally Turkey.
Russia sees Nato as a threat and has warned of “consequences” to expansion.
To join the alliance, the two nations need the support of all 30 Nato member states.
Speaking alongside Swedish Prime Minister Magdalena Andersson and Finnish Prime Minister Sauli Niinisto at the White House on Thursday, Mr Biden called Sweden and Finland’s applications to join Nato “a watershed moment in European security”.
“Let me be clear: new members joining Nato is not a threat to any nation,” he said. “Nato’s purpose is to defend against aggression. Let no one make a mistake on this historic day.”
In the US, new Nato memberships require legislation to pass in Congress with a two-thirds majority.
The decision by both countries to break decades of neutrality with their move to join Nato comes amid rising concerns for their own security following Russia’s invasion of Ukraine. In Finland’s case, the country shares an 810 mile (1,300 km) border with Russia.
The Swedish and Finnish applications to join Nato, however, have been opposed by Turkish President Recep Tayyip Erdogan.
“We are open to discussing all the concerns Turkey may have,” President Niinisto said. “We condemn terrorism in all its forms and we are actively engaged in combating it.”
Mr Erdogan has said Swedish and Finnish delegations should not bother going to Ankara, Turkey’s capital, to convince it to approve their Nato bid.
However, both Nato secretary-general Jens Stoltenberg and British defence minister Ben Wallace have expressed confidence that Turkey’s concerns will eventually be addressed.
On Thursday, the US Senate approved a $40bn (£32bn) bill to provide military and humanitarian aid to Ukraine.
The bill – which was passed by the House of Representatives with broad bipartisan support – was expected to be passed earlier this week, but was blocked by Kentucky Republican Rand Paul over dispute about spending oversight.
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