NAIROBI—Kenya's election commission on Saturday declared Uhuru Kenyatta the country's next president, handing control of East Africa's biggest economy to a man charged with crimes against humanity.

Final results showed Mr. Kenyatta triumphed with 50.07% of 12.3 million votes cast, a whisker above the 50% margin he needed to avoid a runoff. Some 86% of Kenya's more than 14 million registered voters turned out for Monday's elections, a record in the country's five decades of independence.

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