The law, which rolls back Putin's previous time in office to now stand at zero, was published on a government portal on Monday.
The State Duma passed the law in late March, implementing a key point of the controversial new constitution that Russians voted on in July.
Under the previous 1993 constitution, Putin would have had to leave the Kremlin in 2024. But by annulling his previous terms in office since 2000, the 68-year-old can now run in the next two presidential elections - and theoretically continue to govern Russia until 2036.
More powers
The biggest constitutional restructuring in Russian history also gave Putin significantly more powers.
At the time, Russian opposition members accused the president of abusing his power and overthrowing the constitution.
