Long queues formed early on Sunday morning outside polling stations in the capital, Dakar – home to more than 1.6 million of 6.6 million registered voters.
Voting centres opened at 08:00 GMT and closed at 18:00 GMT, with preliminary results out on Tuesday and the official tally out on Friday.
A candidate must secure more than 50 percent of the votes to be declared the winner.
If no contestant wins a majority, a runoff between the two leading candidates will be held on March 24.
President Macky Sall, who came to power in 2012, is widely expected to win the poll.
Sall, who is seeking a second and final term in office, became the frontrunner after two of Senegal’s most well-known opposition leaders were barred from running in the election.
The former mayor of the capital, Khalifa Sall, who is not related to the president, is serving a five-year jail term on corruption charges, while Karim Wade, son of the country’s former leader Abdoulaye Wade, has gone into exile in Qatar after serving half of a six-year jail term for corruption.
Both deny the charges, which they say are politically motivated.
Sall, Senegal’s first president to be born after the country got independence from France in 1960, has promised his supporters “victory in the first round” of voting.
“This voting day is a very important moment for the democratic cycle. It is an illustration of popular sovereignty. I’m asking you to accomplish your duty as citizens in peace and calm in order to decide what we will do over the next five years,” Sall said, speaking after casting his vote at a polling station in his home town of Fatick.
Sall is facing competition from four other candidates.
Candidate Madicke Niang told his supporters after casting his ballot in the city of Touba that he was sure of victory.
“I have just performed my civic and citizen duty which is voting. Long live the republic, Long live Senegal. We will meet tonight when we win.”
Meanwhile, the European Union which had observers across Senegal said there were no major incidents at the polling stations it observed.
“Almost all the polling stations observed were positively assessed by EU observers, who noted that voters were familiar with the voting procedures and that the performance of polling station staff was satisfactory,” Elena Valenciano, chief of EU observer mission in Senegal, said in a statement.
“Voter turnout at the polling stations observed was rated as good, particularly in urban areas,” Valenciano added.
Senegal is one of the most stable democracies in Africa and has had three peaceful transfers of power since independence.