Justices rejected several petitions challenging the vote, including an appeal by Prime Minister Raila Odinga, Kenyatta's main rival, the BBC reported.
The official tally said Kenyatta beat Odinga 50.07 percent to 43.28 percent, avoiding a runoff by 8,100 votes. Odinga's lawyers had argued the election was riddled with vote manipulation, as well as problems with an electronic vote counting machine and voter registration.
Despite those issues, the Independent Electoral and Boundaries Commission declared the vote credible. International observers said the commission had conducted the election in an open and transparent manner.
An estimated 1,200 people died following a contested election in 2007, leading outgoing President Mwai Kibaki to urge Kenyans to remain calm and accept the court's decision in the latest election.
Kenyatta's win complicates diplomatic ties with the West, CNN reported. He and his running mate, William Ruto, are accused by the International Criminal Court of crimes against humanity stemming from violence in the 2007 election.
The Obama administration issued a statement congratulating Kenyatta and urging Kenyans to accept the outcome peacefully.
"The electoral process and the peaceful adjudication of disputes in the Kenyan legal system are testaments to the progress Kenya has made in strengthening its democratic institutions, and the desire of the Kenyan people to move their country forward," White House press secretary Jay Carney said in a statement on behalf of Obama.
"Now is the time for Kenyans to come together to fully implement the political, institutional and accountability reforms envisioned in the Kenyan Constitution."