President Vladimir Putin signed the bill on Saturday, while also signing a legislation that makes it prohibited to spread information that encourages people not to have children.
The new laws have previously been approved by Russia's parliament.
The State Duma's speaker Vyacheslav Volodin has in previous statements on social media claimed that it is "important to eliminate any dangers in the form of gender change that adopted children may be exposed to in these countries".
The adoption ban will affect at least 15 countries, most of them in Europe.
In recent years, Putin has pursued an increasingly restrictive policy towards sexual minorities, and through state decrees has promoted "traditional values", partly as an attempt to counteract Russia's population decline.
