The Conseil de Paris on Tuesday agreed to adopt a plan that will see the current ground, which can hold 9,200 spectators, demolished next year and rebuilt by 2011 - at a cost of an estimated 111million euros (Â£75m).
During the reconstruction work, Stade could play their home games at a stadium in Charlety or, for bigger matches, at the nearby Parc des Princes or even the Stade de France.
Club president Max Guazzini, a leading advocate of these proposals for a number of years, told L'Equipe: "This is good news, not just for Stade Francais. It is a victory for rugby in France.
"We know there will be a true rugby stadium in Paris, with facilities worthy of the name, which isn't the case today."
As well as doubling the capacity inside the stadium, a new administrative centre and a parking area accommodating 500 places will be built.
Stade have often resorted to playing their major matches in the Top 14 or the Heineken Cup at either the Parc des Princes or the Stade de France, because of the inferior facilities at the Jean-Bouin.