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).
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. Crowds cheered the motorcade along its route.
At dinner, the president was joined by more relatives, including the woman known as “Granny” or “Mama Sarah”, who helped raise his now-deceased father.
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 US 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.
Kenya means a lot to President Obama – here they call it his homecoming – and he has both his heritage and his legacy to consider late in his final term.
His first engagement is a global entrepreneurial summit – better business and trade, not aid, are how he sees many Africans lifting themselves out of poverty.
But security remains America’s top priority while al-Shabaab can still kill students in their dormitories. And just two years after the Westgate shopping centre attack, security co-operation will dominate discussions.
Mr Obama has promised tough talking on good governance, human rights and corruption.
President Kenyatta’s International Criminal Court indictment has been dropped, but his deputy is still facing charges over post-election violence. What’s more, he’s warned America not to lecture Kenyans on gay rights.
The interaction could be awkward, and with rights firmly on the American agenda there may be more to this trip than just smiles and photo opportunities.
Mr Obama expanded on his hopes for the Africa trip in a wide-ranging interview with the BBC’s North America editor Jon Sopel before he left Washington. President Obama also said:
- His failure to pass “common sense gun safety laws” in the US was the greatest frustration of his presidency
- The UK must stay in the EU to have influence on the world stage
- He is confident the Iran nuclear deal will be passed by Congress
- Syria needs a political solution in order to defeat the Islamic State group
- Despite racial tensions, the US is becoming more diverse and more tolerant.