Weighing into a dispute over a hike in taxes, Putin heaped praise on Depardieu, making the offer of citizenship in response to a question during his annual televised press conference.
"If Gerard really wants to have either a residency permit in Russia or a Russian passport, we will assume that this matter is settled and settled positively," Putin said.
French daily Le Monde reported on Tuesday that Depardieu had told his close friends he was considering three options to escape France's new tax regime: moving to Belgium, where he owns a home, relocating to Montenegro, where he has a business, or fleeing to Russia.
"Putin has already sent me a passport," Le Monde quoted the actor as jokingly saying.
Depardieu is well-known in Russia where he has appeared in many advertising campaigns, and in 2012 he was one of several Western celebrities invited to celebrate the birthday of Ramzan Kadyrov, Chechnya's Kremlin-backed leader.
He also worked in Russia last year on a film about the life and times of the eccentric Russian monk Grigory Rasputin.
He has already inquired about how to obtain Belgian residency rights and said he plans to hand in his French passport and social security card.
In what has become an ugly public dispute, France's Prime Minister Jean-Marc Ayrault criticised Depardieu's announcement as "pathetic" and unpatriotic. The actor hit back, accusing France of punishing success and talent.
But Putin said he thought the feud was the result of a "misunderstanding".
The 60-year-old former KGB spy said he was very friendly with Depardieu, saying he thought the actor considered himself a Frenchman who loved the culture and history of his homeland.
Belgian residents do not pay a wealth tax, which in France is now levied on those with assets over 1.3 million euros ($1.7 million). Nor do they pay capital gains tax on share sales.
Hollande is also pressing ahead with plans to impose a 75-percent super tax on income over 1 million euros.
Russia has a flat income tax rate of 13 percent.
(Reporting by Alexei Anishchuk; Additional reporting by John Irish in Paris; Writing by Gabriela Baczynska; Editing by Alissa de Carbonnel and Andrew Osborn)