The governing coalition's candidate, former prime minister Amadou Ba, finished with 35.79 percent, and the Council said no objections had been raised by the other contenders.
Faye, 44, is due to be sworn in as Senegal's youngest president on Tuesday in the city of Diamniadio, according to the presidency.
The handover of power with outgoing leader Macky Sall is then scheduled at the presidential palace in the capital Dakar.
Faye's victory is the first time a Senegalese opposition candidate won the election in the first round since independence in 1960.