Peter Obi, Labor's presidential candidate, came in third among the top three contenders, pulling in 6.1 million votes.
The winner, All Progressives Congress [APC] candidate Bola Tunubu, won 8.8 million ballots, with 6.9 million going to the second-place finisher, opposition Peoples Democratic Party (PDP) nominee Atiku Abubakar.
"The purported results did not meet the minimum criteria of a transparent, free and fair election," said Obi's running mate, Yusuf Datti Baba-Ahmed.
"We will go to court," he said, while urging supporters to "remain peaceful and calm".
Candidates who want to contest the election have 21 days following the announcement of results to bring their case to the courts.
The Labor Party's election legal contentions have not been specified to the media yet.
Outgoing President Muhammadu Buhari has called on the losing parties and their candidates to remain calm and respect the findings issued by Nigeria's Independent National Electoral Commission [INEC].
This report was sourced from Reuters and Agence France-Presse.