Sall had until now remained coy about his ambitions, stoking tensions over whether he would use a constitutional revision to argue he could extend the country's traditional two-term maximum.
"My dear fellow citizens, my decision after long consideration is to not be a candidate in the election on February 25, 2024," Sall said in a televised address.
"Senegal is more than me, and is full of capable leaders for the country's development," he said.
Sall said he had sought to prioritize his country's progress, "in particular at a time of social-economic difficulties and uncertainties."
On the eve of Sall's nationwide address, his fiercest critic, Ousmane Sonko, had urged the public to "come out en masse" and oppose him.
Deadly clashes erupted last month between Sonko supporters and the security forces, claiming at least 16 lives.
The turbulence tarnished Senegal's image as a beacon of stability in West Africa.
Sall, 61, was first elected in 2012 for a seven-year term and again in 2019 for a five-year term, following a constitutional revision of the presidential tenure.
The constitution stipulates that a president cannot serve more than two terms -- but Sall's supporters had argued the counter had been reset to zero thanks to the 2016 revision.
Sall had previously campaigned against a third term by his predecessor, Abdoulaye Wade, who was in power from 2000 to 2012, and had said he would not seek re-election, bucking the continent's trend of entrenched strongmen leaders.
But he had not designated a political successor, and in recent months has been coy about another term, a position that has stoked tensions.
Sonko, a fiery orator popular with Senegal's disaffected youth, has painted Sall as a corrupt, would-be dictator.
"It's incumbent on all the Senegalese people to stand up, to face him," Sonko said on Sunday.
Sonko was sentenced on June 1 to two years' jail for "corrupting" a young beauty salon worker, sparking protests which led to 16 deaths according to the government, 24 according to Amnesty International, and 30 according to Sonko's party.
The conviction makes him ineligible to stand in 2024.
Sonko says the case was staged to prevent him from running, a charge authorities deny. He has been blocked in by the authorities at his home since May 28.