The move follows clearance of the acquisition by the European Commission, and values the company at £4.5 million.
The French spirits giant has set up The Absolut Company as part of its network of brand-owning operations that includes Chivas Brothers, Irish Distillers and Martell Malibu-Kahlua International.
V&S Absolut Spirits president Ketil Eriksen will be chief executive officer of the vodka brand company.
As a result of the Absolut deal, Pernod will end the distribution rights it had for Stolichnaya vodka in the UK and other markets outside Russia.
Patrick Ricard, chief executive officer of Pernod Ricard, said: “This operation will substantially accelerate the growth of both the Absolut brand, which will benefit from the group’s worldwide distribution network, and Pernod Ricard.”