The legislation was passed by Russia's lower house of Parliament last month and Putin signed it on Monday, The Moscow Times reported.
The legislation, which will come into force in July 2020, is dubbed the "law against Apple" due to the iPhone maker's refusal to sell products loaded with such apps.
But before the legislation comes into force, the government will have to make a list of apps that need to be pre-installed and also provide a list of devices that will be covered by the law.
Smartphones, computers, tablets and smart TVs are expected to be covered by the law, according to the report.
Supporters of the legislation argue that it will give Russian consumers more choice and make it easier for them to use the devices that they purchase, while giving the Russian technology industry a level playing field to compete with foreign tech firms.
However, the legislation also raised concerns over surveillance and triggered speculation about some companies exiting the Russian market.
Apple reportedly earlier threatened to leave the Russian market if it is completely banned from selling products without pre-installed Russian apps.
According to a report in the Meduza news website, companies will face a fine of 200,000 rubles ($3,100) for not abiding by the law.
( With inputs from IANS )