Gazprom chief executive Alexei Millar said the Total would hold a 25% stake in the company controlling the infrastructure of the field.
The two firms are expected to sign an agreement on the project on Friday.
The gas field in the Barents Sea - holding an estimated with 3.2 trillion cubic metres of gas - could become the world's largest offshore gas field.
As the project gets under way further partners could be given a 24% share in the development, Mr Millar added.
Other companies that could join the project include Norway's Statoil and Norsk Hydro as well as US group ConocoPhillips.
Rising demand
Gazprom is the monopoly supplier of gas in Russia, and is playing a key role in supplying the rest of Europe with gas supplies.
Demand for natural gas is expected to rise sharply, while other European sources of natural gas, such as the North Sea, are likely to decline.
And much of the gas in the Shtokman field could be sent to meet Europe's growing needs, either through a pipeline or through tankers sailing from the ice-free port of Murmansk and carrying liquidifed natural gas (LNG).
"The agreement that has been reached is the latest important step in developing mutually beneficial cooperation and partnership relations between Gazprom and the world's biggest energy companies," Mr Millar said in a statement.
Gazprom's choice of a partner for the Shtokman field is a distinct turnaround from its position in October 2006 when the Russian firm said it had decided that it alone would exploit the huge untapped gas reserves.
U-turn
However, earlier this week one of the group's top executives Alexander Medvedev signalled that Gazprom had once again changed its mind about the project.
In an interview with the Financial Times newspaper he said Gazprom was in talks with foreign companies to allow them to "share in the economic benefits of the project, share the management and take on a share of the industrial, commercial and financial risks".
The cost of the operation has been estimated at between $20bn (£10bn) and $30bn which Gazprom would have to foot if it decided to go it alone.
Commentators claim that the complexities of the project - including Gazprom's lack of experience with LNG, harsh weather conditions and lack of infrastructure to transport the gas to market - had led to Gazprom's U-turn.