No legal challenge to the outcome of a presidential election has succeeded in Nigeria, which returned to democracy in 1999 after three decades of almost uninterrupted military rule and has a history of electoral fraud.
Atiku Abubakar of the People's Democratic Party and Peter Obi of the Labour Party, who came second and third respectively, had asked the court to cancel the election, alleging irregularities.
Justices of the five-member tribunal, taking turns to read out judgements for more than 11 hours, rejected Atiku and Obi's individual petitions point-by-point.
Judge Haruna Tsammani said Obi's petition was "unmeritorious" and had "not led any credible evidence sufficient enough" to back claims of irregularities.
Tsammani said Atiku's allegations of vote fraud were "so lame" and dismissed his argument that Tinubu was not qualified to run for president.
"The petitions are hereby dismissed," Tsammani said.
Obi and Atiku, who were not in court, could not be immediately reached for comment.
Obi's Labour Party in a statement rejected the judgment and said it would announce its next steps after a meeting with lawyers.
In a statement from India where he is preparing to take part in the G20 summit, Tinubu welcomed the tribunal ruling and urged his rivals and their supporters to support his government.
European Union observers had said in June that the elections were marred by problems including operational failures and a lack of transparency that reduced public trust in the process.
However, the elections stirred little sign of a groundswell of popular opposition, and Tinubu has been accepted by the international community as Nigeria's legitimate leader.
Atiku and Obi can appeal to the country's Supreme Court to strike down the tribunal's ruling.
Any appeal must be concluded within 60 days of the date of the tribunal judgment.
While favourable to Tinubu, the tribunal's ruling was unlikely to generate any particular euphoria or momentum for the president after an election marked by record low turnout of 29 per cent.
In a country of more than 200 million people of whom 87 million were registered to vote, Tinubu garnered just 8.79 million votes, the fewest of any president since the return to democracy, limiting the goodwill towards him.
