Mutko was the only candidate in the election after State Duma vice-speaker Igor Lebedev, the only other person who had registered, pulled out at the end of July.
"I have been working as the sports minister for seven years already. However, given the situation that has occurred within our football, I decided to take up the challenge," Mutko told the conference.
"The most important thing is to pay off the debts that the RFU owes and they are huge. I don't want to dramatise the situation, but we are basically on the edge of going bankrupt," the new RFU president added.
"The first step I will take at the RFU will be to make sure that football is going in the right direction. It is not very good when no one understands who and where all the decisions are being taken."
Mutko was president of the RFU from April 2005 until November 2009. The organisation was subsequently run by Sergei Fursenko and Nikolai Tolstykh.
Tolstykh left his post on May 31, following a vote of no confidence from RFU members.
"Mutko is the best candidate for the post of the RFU president," said Nikita Simonyan, who had been the acting head of Russian football's governing body for the last three months.
"This is certainly the case given his experience. He has been the president of Zenit, then was in charge of the Premier League and the RFU. No one will be able to organise the 2018 World Cup like he will be able to."
The RFU president will hold office for one year and new elections will be held in 2016 to elect a head for a four-year term.
(Editing by Sudipto Ganguly)
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