Pozdnyakov, who had served as the committee's first vice-president since 2016, led the Russian delegation at this year's Pyeongchang winter Olympics.
The country was banned by the International Olympic Committee (IOC) as punishment for alleged state-sponsored doping at the 2014 Sochi winter games. But some Russian athletes with no history of doping were cleared to compete as neutrals.
Pozdnyakov, a five-time Olympic medallist, replaces Alexander Zhukov, whose eight-year tenure coincided with the wave of allegations of doping in Russian sport.
Days after Pyeongchang, the IOC lifted the ban against Russia despite two Russian athletes testing positive for banned substances at the South Korean games.
Pozdnyakov beat former Olympic swimmer Alexander Popov, the only other candidate for the post, in a vote at Russia's Olympic Committee in Moscow, the committee said.
Pozdnyakov said the committee would focus on retrieving the trust of the international sports community.
"Our main task is to mend relations (with global sports bodies) through the return of trust in the Russian Olympic Committee," Pozdnyakov told reporters after the vote. "We will pay the most careful attention to this."
Pozdnyakov added that the committee was preparing an educational programme to persuade athletes starting at the grassroots level not to take performance-enhancing substances.
Zhukov, who was suspended as an IOC member last year when Russia was banned, said this month he would not seek reelection.
Russia has denied state-sponsored doping and has pledged to work with international sports bodies to help curb doping.
The country's athletics federation, its anti-doping agency RUSADA and its Paralympic Committee remain suspended by international sporting bodies over doping allegations.
(Reporting by Gabrielle Tétrault-Farber; Editing by Andrew Roche and David Holmes)
