Eni has granted Gazprom the right to acquire the Gazprom Neft stake and 51 per cent stakes in the other three companies within the next two years, the statement said.
The purchase marked Eni's "entrance into the Russian upstream market as a major player and is the third-largest foreign acquisition to date in Russia's oil and gas sector," the company said.
Alexander Medvedev, Gazprom's deputy chief executive, confirmed his company's intention to buy the Yukos assets from Eni, the RIA Novosti news agency said.
Last November, Gazprom and Eni signed a strategic accord that guarantees Gazprom direct access to Italy's market and also guarantees gas supplies to Italy until 2035.
At the auction Eni beat off two other companies, Nefttradegroup, a subsidiary of state-controlled Rosneft, and Unitex, a company that reportedly represented independent gas producer Novatek, which has close ties to Gazprom.
The price paid was only slightly above the starting price of $5.6bn suggesting competition was not intense.
The Kremlin has been anxious to ensure that Western companies participate in the Yukos auctions in order to lend credibility to the company's break-up.
The auctions are the final stage of the Russian government's dismemberment of Yukos, Russia's former number one oil producer, which began when Khodorkovsky was arrested in OCtober 2003.
Khodorkovsky is serving an eight-year sentence in Russia's Far Eastern province of Chita for financial crimes. Other associates of the company have also been jailed.
Robert Amsterdam, Khodorkovsky's lawyer, described said the auctions were an attempt "to legitimise criminal conduct on behalf of Russian officials at the highest levels".
Yukos' main production unit, Yuganskneftegaz, was sold at auction in 2004 to a shell company that was purchased by Rosneft shortly afterward, propelling it to the number three Russian oil producer.
The company, together with Gazprom, is expected to dominate the auctions of Yukos' remaining assets: the Tomskneft production unit and three refineries will be available in early May.