"The debt will be reimbursed before August. Before the end of the summer, Russia will no longer be a client of the Paris Club," he told Interfax, Russia's state news agency.
Kudrin added that the early repayment would mean Russia would save $7.7 billion dollars in debt servicing to the club.
The Paris Club, an informal group which comprises 19 countries including Russia, had agreed in May on the principle of an early payment by Moscow, which is experiencing booming oil and natural gas sales.
However some creditor countries, Germany in particular, had resisted the Russian proposal to pay early because they would lose money on interest no longer paid.
The German government had counted on interest being paid until 2015 in its budget provisions.
Peter Westin, chief economist at the MDM investment bank, said Russia's move was a "positive thing" and a sign that Russia was becoming "one of the strongest emerging markets in the world from a macro point of view".
Westin added that he expected all the major credit rating agencies would review Russia's sovereign debt rating upward this year as a result of the deal, bringing money into Russia's bond market.