The 60-year-old Frenchman replaces Joseph Koto, who was removed from the post after the Lions failed to qualify for this year's African Nations Cup.
Giresse will be in charge of the Lions for the next two years, with qualification for the 2014 World Cup in Brazil first on the agenda.
"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."
Giresse has previously coached Gabon and Mali, leading the latter to a third-placed finish at the 2012 African Nations Cup.