Vivendi said it would also pay Vodafone an extra 200 million euros, reflecting the generation of cash between Jan. 1 and July 1, 2011.
The accord gives Vivendi CEO Jean-Bernard Levy something he has long craved: full ownership of the company's largest business unit, which generates nearly half its profits.
Post-buyout, Vivendi would deliver higher cash flows and stronger profits, and could raise its dividend. The new face of Vivendi is also more exposed to telecoms and its mature home market of France.
For Vodafone, the sale is part of a trimming of its portfolio, done under investor pressure, after a wide international expansion undertaken in the last decade.
The group has already sold its minority stake in China Mobile and begun a sale process of the nearly 25 percent it owns of Poland's Polkomtel.
The two sides agreed on a price that puts SFR at an enterprise value of 6.2 times 2010 EBITDA.
Analysts are likely to see that as a good outcome for Vodafone, which has been signaling since last year that it wanted about 6 times EBITDA for its stake.
In its statement on Sunday, Vodafone said it would return 4.5 billion euros of the net proceeds to shareholders by way of a share buy-back. The rest of the proceeds would go to reducing the group's debt.
For Vivendi, the price tag for SFR is also likely to allow it to keep its current credit rating, something its CEO had long pledged to preserve. Fitch Ratings earlier this year said it could pay up to 6.5 times EBITDA without affecting its rating.
Vivendi will pay for the SFR deal in part from the $5.8 billion it received in January for selling its 20 percent holding in NBC Universal in the US, as well as the 1.25 billion euros it got from settling an ownership fight over a Polish telecom operator PTC.
Both companies said in separate statements on Sunday that the deal was expected to close by the end of June 2011 and was subject to regulatory approval.