Dignitaries and tens of thousands of people witnessed the inauguration at a stadium in the capital, Nairobi.
Raila Odinga did not attend the ceremony after his attempt to overturn Uhuru Kenyatta’s victory in court failed.
Uhuru Kenyatta and his deputy, William Ruto, face charges at the International Criminal Court relating to post-election violence five years ago.
They were on opposite sides at the time and both deny the accusations.
Sudanese President Omar al-Bashir, who faces an ICC arrest warrant over the conflict in Darfur, was not in Nairobi for the inauguration.
Uhuru Kenyatta, 51, is the son of Kenya’s founding father, Jomo Kenyatta, and is heir to one of the largest fortunes in Kenya.
He served as deputy prime minister, minister for trade, and finance minister under outgoing President Mwai Kibaki
The crowd, waving Kenyan flags, burst into rapturous welcome as Uhuru Kenyatta took the oath of office, becoming Kenya’s youngest president.
In his inaugural address, Uhuru Kenyatta said he would govern for all Kenyans.
“We will leave no community behind… Where there’s disillusionment, we’ll restore hope,” he said.
The new government would abolish maternity fees in its first 100 days and children starting school next year would be given laptops, he added.
In an apparent reference to the ICC case against him, Uhuru Kenyatta said: “I assure you again that under my leadership, Kenya will strive to uphold our international obligations, so long as these are founded on the well-established principles of mutual respect and reciprocity.”
US and European diplomats attended the inauguration, despite warning before the election that they would have limited contact with Uhuru Kenyatta if he is voted into office.
Among the African leaders present for the inauguration were South Africa’s Jacob Zuma, Nigeria’s Goodluck Jonathan and Uganda’s Yoweri Museveni.
Yoweri Museveni told the cheering crowd that he wanted to applaud Kenyans for rejecting the “blackmail” of the ICC.
He supported the ICC when it was formed, but it was now being used by “arrogant actors” who were trying to “install leaders of their choice in Africa and eliminate those they don’t like”, he said.
Raila Odinga – the outgoing prime minister – did not attend the ceremony, choosing to be on holiday in South Africa instead.
Other senior members of his Coalition for Reforms and Democracy (CORD) party have also stayed away to signal their opposition to Uhuru Kenyatta’s presidency, correspondents say.
According to official results, Uhuru Kenyatta beat Raila Odinga by 50.07% to 43.28% in March, avoiding a run-off by just 8,100 votes.
Raila Odinga challenged the result, but said he would respect the Kenyan Supreme Court’s ruling in Uhuru Kenyatta’s favor.
The election was Kenya’s first after a disputed poll in 2007, which led to violence that left more than 1,200 people dead.
Uhuru Kenyatta is due to appear at the ICC for his trial in The Hague later this year, accused of crimes against humanity. He denies the charges.
Kenya is a party to the Rome Statute, the treaty which established the ICC in 2002.
But like most African countries, it has refused to enforce the ICC warrant for Omar al-Bashir’s arrest.
After Omar al-Bashir visited Kenya in 2010, a Kenyan court ruled that the government must arrest him if he returned, in line with its international obligations under the Rome Statute.
The government is appealing against the ruling.
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