The AIIB is an international financial institution hosted by China to invest in infrastructure projects in the Asia-Pacific region. A bill establishing the bank with a registered capital of up to $100 billion was signed by 21 countries in October 2014.
"Russia and Finland will become founding members on April 14 and April 12, respectively, should all existing members approve," the Council said in a statement published on its website.
The bank has 45 member states, with March 31 being the deadline for applications to become a founding member.
The creation of the AIIB has attracted numerous countries across the world, including the United Kingdom, Australia, India and Saudi Arabia.
The Chinese-led project has raised concerns in the United States that it would create competition for Western financial institutions, with Washington reportedly exerting diplomatic pressure to stop its allies from joining the bank.