The inauguration took place on Tuesday in the presence of hundreds of international delegations and African leaders including Nigeria’s President Bola Tinubu.
“Before God and the Senegalese nation, I swear to faithfully fulfil the office of President of the Republic of Senegal,” the 44-year-old said.
Faye emerged victorious at the polls and the Senegalese ruling party candidate Amadou Ba conceded defeat to him.
Ba had released a statement congratulating Faye while wishing him well.
The poll was earlier scheduled for 25 February, but it was shifted indefinitely by the outgone president Macky Sall on 3 February.
Sall had alleged irregularities with the way political parties selected their candidates.
But his directive was set aside by the Senegalese Constitutional Court and following international pressure.
Faye, a 44-year-old activist, had promised citizens a lucrative oil and gas revolution if elected.