The polls have been seen as a test case of the reputation for stability that Senegal has enjoyed since French rule ended in 1960.
Senegal is considered a regional oasis of democracy and is the only country in the volatile region to have never experienced a coup.
Opposition to contest results
The socialists, who ruled the west African country for 40 years until Wade first defeated them in 2000, accused the government of committing fraud in Sunday's poll and said they would challenge the results.
"A president who was not elected cannot lead the country," Aissata Tall Sall, a spokeswoman for Socialist leader Ousmane Tanor Dieng, one of Wade's main rivals said late on Tuesday.
"We will not accept these results," Sall told a press conference, stating the Socialist Party would contest them by whatever means "people judge appropriate."
She described the campaign as "the most truncated elections of our history".
Wade, who became president after almost three decades in opposition, beat his former prime minister Idrissa Seck who trailed behind with less than 20 per cent of the votes, followed by the socialist leader.
The Economic Community of West African States (ECOWAS) has given the polls, which largely passed off peacefully, their stamp of approval, declaring the elections "free and transparent".
The polls saw a record turnout of voters put at 75 per cent by officials in the predominantly Muslim country.
But according to Tuesday's figures some 3.35 million people cast their ballots out of about 4.9 million eligible voters.