Former Bordeaux and Marseille star Giresse, 60, has signed a two-year deal, the APS news agency quoted FSF president Augustin Senghor as saying.
As a player, Giresse was in the France side which won UEFA EURO 1984 and was also a FIFA World Cup™ semi-finalist in both 1982 and 1986. He has to date coached Toulouse, Paris Saint-Germain and Morocco's FAR Rabat as well as the national teams of Georgia, Gabon and Mali, where he was in the hotseat until last May.
Libya had also made an offer for his services, proposing a one-year deal and he travelled to Tripoli in December while Senegal sought to whittle down a field for their post of Giresse, Senegalese Aliou Cisse, Frenchman Jacques Santini, German Volker Finke and Eriksson.
Giresse replaces Senegalese Joseph Koto, only appointed last June but sacked in October after the Lions were eliminated on the road to the CAF Africa Cup of Nations.
"Giresse is the coach who best meets the criteria defined by the Senegalese Football Federation," FSF president Augustin Senghor told the media. "He has a proven track record at the highest level in Africa."