Sergei Syrtsov, who had been in charge since 2010, quit in September after taking the blame for a large number of doping offences involving the country's weightlifters.
The International Weightlifting Federation (IWF) banned Russian weightlifters in July from competing at this year's Olympic Games.
Three Russian weightlifters were among athletes stripped on Monday of Olympic medals won at the London Games in 2012.
Agapitov, who had been acting RWF President, was standing for election against Mikhail Stepanyants, the first Vice President of the Russian Curling Federation. Agapitov received 43 votes from the 68 delegates.
(Reporting by Dmitriy Rogovitskiy, editing by Ed Osmond)
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