Turkey will begin the process of ratifying Finland's Nato membership, President Recep Tayyip Erdogan said on Friday.
He said Sweden's application would have to wait for further talks. Almost simultaneously, fellow holdout Hungary said it would hold a vote on Finland's bid on March 27.
The US welcomed Mr Erdogan’s announcement and said it looked forward to the prompt conclusion of the approval process.
Announcing the breakthrough after 10 months of negotiations, Mr Erdogan said Finland had taken “authentic and concrete steps” to address Turkish security grievances.
“Nato will become stronger with Finland's membership, and I believe it will play an active role in maintaining global security and stability,” he said.
Turkey and Hungary are the last Nato members to give their verdict and their moves pave the way for Finland to become the 31st member of the military alliance.
Speaking alongside Mr Erdogan on a visit to Ankara on Friday, Finnish President Sauli Niinisto said it was “very good to hear this news”.
But he said Finnish membership in Nato “is not complete without Sweden” because of their shared security interests.
Finland's bid could be approved before Turkish elections in May, while Sweden is not expecting a verdict before then.
“We encourage Turkey to quickly ratify Sweden’s accession protocols as well,” the White House said.
“In addition, we urge Hungary to conclude its ratification process for both Finland and Sweden without delay. Sweden and Finland are both strong, capable partners that share Nato’s values and will strengthen the alliance and contribute to European security.
“The United States believes that both countries should become members of Nato as soon as possible.”
Hungary's ruling party will vote “unanimously yes” on Finland but “decide later” on Sweden, said its parliamentary leader Mate Kocsis.
Senior Nato figures welcomed what Secretary General Jens Stoltenberg said would be the fastest accession in the alliance's modern history despite the delays.
“I look forward to a rapid conclusion of the accession process, and to welcoming both Finland and Sweden to the Nato family as full members as soon as possible,” Mr Stoltenberg said.
Sweden and Finland turned a page on decades of non-alignment to seek Nato membership after Russia's invasion of Ukraine.
They hoped to enter jointly but Turkey's objections to their security and counter-terrorism policy have delayed the process.
Turkey sought a harder line from both countries on Kurdish dissidents that it considers terrorists, while the public burning of a Quran in Sweden further aggravated Mr Erdogan.
He said on Friday that Turkey had sent Sweden a list of 120 alleged terrorists but that none had been extradited.
“How the process will progress will be directly linked to the concrete steps which Sweden will take,” he said.
Hungary, which has several quarrels with Nato and the EU, has long delayed scheduling a vote despite saying it supports Finland and Sweden.
Prime Minister Viktor Orban last month accused them of “blatant lies” about democracy and the rule of law in Hungary.
Sweden's Foreign Minister Tobias Billstrom said it regretted Turkey's decision to hold off moving forward on his country's Nato bid, while pushing ahead with that of Finland.
“This is a development that we did not want, but that we were prepared for,” Mr Billstrom said.
Allies have offered assurances that they would assist Sweden if it were attacked before joining Nato.
The UK “will stand shoulder to shoulder with Sweden against any Russian intimidation,” Britain's Defence Secretary Ben Wallace said on Friday.
Finland and Sweden already carry out joint exercises with Nato and regularly attend alliance meetings.
Full membership will bring them under the protection of Nato's Article 5 mutual defence guarantee. US President Biden has promised to defend “every inch” of alliance territory.
Finland's accession will more than double the length of Nato's land border with Russia, in what alliance leaders have described as a case of backfiring Kremlin policy.
Kremlin spokesman Dmitry Peskov said on Thursday that Russia posed no threat to Finland or Sweden and regretted their requests to join Nato.