During his two-day visit Mr Obama will hold talks with Kenyan President Uhuru Kenyatta and other top officials.
Trade will feature strongly, but Mr Obama also said he would deliver a "blunt message" to African leaders about gay rights and discrimination.
The trip to Kenya and then Ethiopia is also designed to show US commitment to fighting terror in East Africa.
President Obama's Air Force One touched down at Nairobi's international airport shortly before 20:10 local time ( 17:10 GMT).
President Obama (centre) was also greeted by his half-sister Auma at the airport
Arriving in the country where his father was born, he was greeted at the airport by President Kenyatta with a handshake and embrace.
Mr Obama also hugged his half-sister Auma, who then travelled in the presidential limousine to the hotel where the US leader is staying.
Security is tight. The Kenyan capital is in lockdown, many streets are closed and people are opting to stay at home.
Mr Obama, the first sitting president to visit Kenya, will hold talks on trade and investment, and also security and counter-terrorism.
He also becomes the first US leader to address the African Union when he travels on to Ethiopia on Sunday.
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