The March 4 general elections – for the presidency, regional governors, senators, members of parliament as well as local councillors – were marred by allegations of vote rigging.
Defeated candidates have also raised concerns about the widespread failure of an electronic voter registration system – designed to limit fraud – as well as of the electronic transmission of results, which forced a manual tallying process.
Odinga is expected to request a "forensic audit of manual and electronic data", including investigations into the alleged "drastic reduction and rise" of votes in some constituencies after the official register was closed, a close aide to Odinga said.
He legally has until Saturday to file his petition – seven days from the results – with the Supreme Court then having 14 days to make their ruling.
Kenya's Chief Justice Willy Mutunga has the power to order a recount, order a whole new election or dismiss the petition.
"We are going to listen to all cases brought before us fairly," Mutunga said on Monday.
While many were concerned at the risk of renewed violence ahead of the election, no major incidents have been reported in recent days.
Kenyatta, who avoided a second round run-off vote by the slimmest of margins to win a majority with just 50.07%, beat Odinga – his closest rival – by more than 800 000 votes.
Odinga, who won 43.31% in the March 4 poll in his third failed attempt at the top job, said he will respect the decision of the Supreme Court even if it rules against him.
He has also called for his supporters to allow the legal process to run its course, warning shortly after Kenyatta was declared president-elect on Saturday that "any violence now could destroy the country forever".
Kenyatta, one of Africa's richest men, faces trial for crimes against humanity at the International Criminal Court (ICC) over his alleged role in orchestrating the bloody violence following the 2007 contested elections.
More than 1 100 people were killed and over 600 000 fled their homes in one of the worst bouts of ethnic bloodletting in Kenya.
The peaceful conduct of polls has been praised by the international community, who have also urged that disputes over the results must be done through the courts.
Kenya's neighbours as well as China have offered congratulations directly to Kenyatta, with Beijing on Monday saying it wanted to "strengthen co-operation with the new government", foreign ministry spokesperson Hua Chunying said.
African Union commission chief Nkosazana Dlamini-Zuma on Monday saluted the "people of Kenya for the successful and peaceful" elections, and congratulated Kenyatta and running mate William Ruto, who also faces an ICC trial.
But Western nations – who have a policy of only essential contact with those charged by the ICC – have praised the Kenyan people while avoiding mention of Kenyatta's win.
United States Secretary of State John Kerry congratulated "all those elected to office", a message echoed by European Union foreign policy chief Catherine Ashton.
If Odinga's petition to the Supreme Court is dismissed, Kenyatta would be inaugurated as Kenya's fourth president one week later, suggesting a possible ceremony in early April.
Kenyatta has offered "my older brother" Odinga an olive branch, telling thousands of his loyalists he wanted to work with him "in moving our nation forward".
He also called on his celebrating supporters to be "modest in our victory".
Kenyatta's trial at the ICC opens on July 9, while Ruto's begins on May 28. – AFP