The decision was passed unanimously by 162 votes in the Federation Council.
"With this decision, we are effectively launching the start of the election campaign," Valentina Matviyenko, head of the Federation Council, said.
She added that for the first time residents of the parts of Donetsk, Luhansk, Zaporizhzhya and Kherson regions of Ukraine annexed by Russia would take part in the vote.
Putin hasn't yet announced his intention to run again, but he is widely expected to do so in the coming days now that the date has been set.
Putin, 71, has been in power as Russia's president or prime minister since the last day of 1999, when Boris Yeltsin stepped down and made him acting president.
Under constitutional reforms he orchestrated, Putin is eligible to seek two more six-year terms after his current one expires next year.
Having established tight control over Russia's political system, Putin's victory is all but assured. Prominent critics who could challenge him on the ballot are either in jail or living abroad, and most independent media have been banned.
Alexei Navalny and Vladimir Kara-Murza, two of Russia's best known opposition politicians, are both serving decades in penal colonies. Many of Putin's other leading critics have fled abroad.
Neither the costly, drawn-out military campaign in Ukraine, nor a failed rebellion by mercenary chief Yevgeny Prigozhin in June appear to have affected his high approval ratings reported by independent pollsters.
The March election clears the way for him to remain in power at least until 2030.
If Putin completes another six-year term in the Kremlin, he will overtake Josef Stalin - who led the Soviet Union from 1924 to 1953 - and become the longest-serving leader of Russia since Empress Catherine the Great in the 18th century.
Opposition politicians see the election as a mockery of democracy, designed to create the appearance of real political competition. Supporters of Putin dismiss that analysis, pointing to independent polling giving him approval ratings of above 80 per cent.
with agencies