The court released the unanimous decision on Saturday.
Uhuru Kenyatta and his running mate William Ruto were "validly elected" during balloting March 4, Chief Justice Willy Mutunga said in court.
The election results were challenged by Kenyatta's rival, Prime Minister Raila Odinga, who is claiming election fraud.
Kenyatta won the election with just over 50 per cent of the ballots.
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