A joint news release said Wednesday: "The deal is worth $13.091 billion."
Prospect Investment analyst Dmitry Mangelev said: "This is the biggest deal not only in the history of Gazpom, but also Russia."
Gazprom earlier bought 3.016% of the shares in Sibneft from Gazprombank.
"Therefore, as a result of the deal, Gazprom will gain control of 75.679% of Sibneft shares," the joint release said.
Sibneft is Russia's fourth largest oil producer. Millhouse is the investment vehicle for Russian tycoon Roman Arbamovich.
Gazprom borrowed a record $12 billion from Western banks last week to finance the Sibneft deal. Three banks - ABN AMRO, Dresdner Kleinwort, and Wassterstein - led the negotiations on the deal and have been joined as underwriters by Citigroup, Morgan Stanley, Goldman Sachs and Credit Suisse. They have each committed $2 billion on the deal, which will be partly refinanced with a Gazprom bond issue.
Sibneft's market capitalization is estimated at $17 billion.