The Central Election Commission will check the authenticity of the signatures and must decide within 10 days whether he can run.
"Millions of people" support his bid, the 60-year-old Kremlin critic said. "I don't understand how these signatures could not be accepted."
Nadezhdin the only anti-war candidate
Nadezhdin has said he did not expect such a "crazy wave" of support.
"People understand that their lives and the safety of their families is threatened by what (Russian President Vladimir) Putin is doing," he said.
Should the election commission reject his bid, he told supporters he is prepared to call for mass protests in 150 cities across the country.
Nadezhdin's call to end the war in Ukraine has also energized the Russian opposition.
Former TV journalist Yekaterina Duntsova was among the first public figures to express support for Nadezhdin's nomination. Her endorsement came after the Central Election Commission excluded her from the race, citing "errors in the documents" submitted. She underscored that Nadezhdin was the only anti-war candidate.
The wife of imprisoned opposition politician Alexei Navalny, Yulia Navalnaya, also signed her name in support of Nadezhdin.
Unlike Navalny, who is serving 19 years in prison, Nadezhdin has not faced any criminal charges for his statements yet.
Putin expected to win
The election's outcome is widely seen as a foregone conclusion, with incumbent President Putin all but certain to win.
"We don't see him as a rival," Putin's spokesman Dmitry Peskov said last week.
Putin registered as a candidate for the March 15-17 election earlier this week, the election commission said.
He has chosen to run as an independent rather than as the candidate of the ruling United Russia party and submitted 315,000 signatures in support of his candidacy.
Nadezhdin said earlier this month that the country would be able to afford to spend more on its citizens if it was not pouring so much money into the military.