The Finnish President said the breakthrough came after the three countries signed a joint memorandum "to extend their full support against threats to each other’s security."
President Erdogan said Sweden should not expect Turkey to approve its NATO bid.
Sweden and Finland need each of NATO's 30 members to approve their applications, including Turkey's president who said he would decline.
The new US president has urged his fellow NATO leaders to stand up to China's authoritarianism and growing military might.