The winner will be tasked with steering Senegal, viewed as a beacon of democracy in coup-hit West Africa, out of its recent troubles and managing revenues from oil and gas reserves that are shortly to start production.
Two favorites have emerged among the 17 candidates who include a sole woman: the governing coalition's former prime minister Amadou Ba and anti-establishment candidate Bassirou Diomaye Faye.
Both were once tax inspectors but Ba, 62, now stands for continuity while the 43-year-old Faye promises profound change and left-wing pan-Africanism.
Both have also pitched themselves as the best candidate for young people in a county where half the population is under 20.
"I voted for Diomaye without thinking," said Diaraaf Gaye, a 26-year-old shopkeeper.
"It's time for the country to start on a new footing with young people" in power.
But 23-year-old housekeeper Ndeye Penda Faye said she was pinning her hopes on the government's candidate.
"(President) Macky Sall has done a lot of work, and that's why I'm going to vote for Amadou Ba, to continue the work," she said.
Voting officially ended at 1800 GMT, with the count starting immediately afterwards, AFP journalists saw in two polling stations in the capital Dakar.
Provisional results could follow overnight, although first official results are expected during the week.
A second-round vote is likely given the number of candidates and the need for an absolute majority, but no date has yet been set.
'Finally got there'
Senegal was originally due to vote on February 25, but an 11th-hour postponement by Sall triggered the worst political crisis in decades that left four dead.
Calm queues formed outside polling stations, with many voters having woken up early to pray before daybreak before heading straight to polling stations.
Voting materials including ballot boxes were still labeled with the original February poll date.
"We finally got there. May God be praised. Recent times haven't been easy for Senegal which has experienced several upheavals," said Mita Diop, a 51-year-old trader.
"But all that is behind us now," she added, emerging from a Dakar polling station with her finger stained in red ink to show she had cast her ballot.
Opposition figurehead Ousmane Sonko — who was barred from standing due to a defamation conviction — said young people had "massively" turned out to vote.
"We are convinced that at the end of this day the victory will be dazzling," Sonko said, referring to his deputy and endorsed candidate, Faye, as he voted in his southern stronghold of Ziguinchor.
"I remain confident about the choice for the change that I am able to embody better than any other candidate," Faye said alongside his two wives, adding he was "convinced" of a first-round victory.
But Faye's adversary Ba is also positive about his chances.
"There is no doubt that at the end of today we should know the next president of the republic," he said after voting in Dakar, adding he was "very, very, very confident."
Calm, efficient
Sall, who is not standing after serving two terms, warned candidates against making premature election victory claims.
"It is neither up to a candidate, nor to a (political) camp to proclaim victory or results," Sall said after voting with his wife in the central western town of Fatick.
Hundreds of observers from civil society, the African Union, the ECOWAS regional group and the European Union are on hand.
The head of the EU mission, Malin Bjork, said that voting had taken place "calmly, efficiently and (in a) very orderly manner."
After weeks of confusion, Senegal's top constitutional body overruled Sall's attempt to delay the vote until December and forced him to reset the date to March 24, resulting in a rushed campaign that clashed with the Muslim fasting month of Ramadan.
Ba, Sall's hand-picked would-be successor, has positioned himself as a last bastion against "bandits" and urged people to vote "for experience and competence instead of entrusting the reins of the country to adventurers."
On Sunday, he spoke of a program of consolidation and acceleration of "everything that has been done so far."
But Sall's legacy also includes mass arrests, persistent poverty, 20-percent unemployment and thousands of migrants setting off on the perilous voyage to Europe each year.
Several episodes of unrest triggered partly by a stand-off between firebrand Sonko and the state have seen dozens killed and hundreds arrested since 2021.
A rapidly passed amnesty law led to the March 14 release from prison of Faye and the charismatic Sonko, who came third in the 2019 presidential poll.
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