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 new constitution that Russians approved in a referendum 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.
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.
Meanwhile, jailed Kremlin critic Alexei Navalny has been moved to a medical facility to be treated for a possible respiratory illness and has been tested for the coronavirus, the Izvestia newspaper has cited the prison service as saying.
He has been diagnosed with a fever of 38.1C and a “severe cough” but he will continue his hunger strike, which he started a few days ago, Navalny wrote earlier on Monday on Instagram.
In February, Navalny was sentenced to several years in prison in a much-criticised trial.
The Russian judiciary accuses him of violating reporting requirements in an earlier criminal case while he was recovering in Germany from an assassination attempt involving the nerve agent Novichok.
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