The meeting, which came after weeks of crisis surrounding the vote, suggested a swift and peaceful handover in the West African nation that prides itself on democratic stability in a coup-hit region.
Faye, 44, was only freed from prison 10 days before the election, along with his mentor Ousmane Sonko, who was barred from running following a criminal conviction he says was politically motivated.
The outgoing president received both men in what his office called "a courteous meeting where they discussed at length the major issues for the state, as well as the inauguration ceremony."
FILE—This picture taken by the Senegalese Presidency on March 28, 2024 shows outgoing Senegalese President Macky Sall (L) greeting Senegal's president-elect Bassirou Diomaye Faye (R) at the Presidential palace in Dakar.
According to provisional results, Faye won the first round of the vote outright with 54.3 percent, far ahead of Sall's hand-picked candidate, former prime minister Amadou Ba.
He came second with 35.8 percent of the vote.
Senegal's Constitutional Court could declare Faye the official winner before the weekend, which would make a handover possible before April 2, the official end of Sall's term.
Sall provoked a political crisis in February by suspending the presidential election just days before polls were to open, citing security concerns.
The move sparked protests and clashes that left four people dead, before the Constitutional Court ordered him to set the date for March 24.
Faye, who has never held elected office, is set to become the fifth president of the West African country of around 18 million people.
He has promised to restore national "sovereignty" and implement a programme of "left-wing pan-Africanism."