The gas produced will "feed into the domestic Iranian market starting from 2021", a Total spokesman said.
Monday's deal will be the culmination of months of negotiations after Total signed a preliminary $US4.8 billion agreement to develop the giant gas deposit alongside its partners late past year.
Qatar's part of South Pars (which it calls the North Field) has been the key to the explosion in its wealth over the last two decades, and has been a big factor in the rise of the global market for liquefied natural gas. The backers are expected to inject an initial $2 billion into the 20-year project to pay for the drilling of about 30 wells and two well-head platforms that will connect the site to onshore processing facilities. Total will develop the project in strict compliance with applicable national and worldwide laws. Upon completion, the field will supply Iran's national grid with 50.9 million cubic meters of gas per day.
The contract will be worth close to $5 billion.
Total had signed up to develop Phase 11 back in 2009 but was forced to abandon its projects in Iran in 2012 when France joined a US-led campaign to put sanctions, including an oil embargo, against the country. But people who work with the company said it is concerned about its exposure to the US and is more selective in the choice of its banks than Total.
"We were here 20 years ago".
Mr Zanganeh said: "We do not consider any obstacle for the participation of American companies".
With sanctions by the USA over weapons, human rights and terrorism still remaining, a number of banks refused to deal with the Tehran and the country's hardliners pushed back against the attempts made by the administration of President Hassan Rouhani to make the terms of for foreign oil companies better. In particular, it must prevent cash flowing to Iran's elite Revolutionary Guards - a tall order given their extensive and shadowy presence across the Iranian economy.
It was in the midst of a 90-day review on whether to stick with the nuclear deal, although any move to abandon it would be strongly opposed by the other signatories Britain, France, Germany, China and Russian Federation.
Foreign Minister Mohammad Javad Zarif was warmly received by European Union leaders last month and tweeted that they were committed to the nuclear deal "despite reckless USA hostility".
A preliminary agreement for the field development was signed in November.
This would allow foreign companies a greater level of certainty and incentive.
But Iran's large population of middle-class consumers presents an irresistible opportunity for many businesses in Europe and beyond.
Iran is one of the third largest producer in the Organization of the Petroleum Exporting Countries (OPEC) and has the second-largest gas reserves and fourth-largest oil reserves in the world.