The 56-year-old-Frenchman has worked previously as national coach of Guinea in two separate spells besides being in charge of Benin.
He has signed a two-year deal with the option for another two years, the federation said in a statement.
Dussuyer replaces compatriot Herve Renard, who left soon after winning the African Nations Cup with the Elephants in Equatorial Guinea in February to take over Ligue 1 club Lille.
Dussuyer was assistant coach of the Elephants , under Henri Michel, when they lost in the final of the 2006 Nations Cup to hosts Egypt on post-match penalties.
Dussuyer’s first assignment will be an African Nations Cup qualifier in Sierra Leone on Sept 5.