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.
BBC Africa Live updates from Kenya
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.
Analysis: BBC’s Alastair Leithead in Nairobi
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.
This is Mr Obama’s fifth trip to Africa as president, but despite his close family links to Kenya, he has faced criticism in some African countries over the legalisation of gay marriage in the US.
However, the president told the BBC he would not fall silent on the issue.
The US leader also agreed that some African governments, including Kenya’s, needed to improve their records on human rights and democracy.
However, he defended his decision to engage with and visit those governments.
“Well, they’re not ideal institutions. But what we found is, that when we combined blunt talk with engagement, that gives us the best opportunity to influence and open up space for civil society.”
- US-Africa ties
“I’ll be the first US president to not only visit Kenya and Ethiopia, but also to address the continent as a whole, building off the African summit that we did here which was historic and has, I think, deepened the kinds of already strong relationships that we have across the continent.”
- Giving the young opportunities
“A while back, when we started looking at strategies to reach out to the Muslim world, to reach out to developed countries, a common theme emerged, which was people are not interested in just being… patronised. And being given aid. They’re interested in building capacity.”
- On China
“We welcome Chinese aid into Africa. I think we think that’s a good thing. We don’t want to discourage it. As I’ve said before, what I also want to make sure though is that trade is benefiting the ordinary Kenyan and the ordinary Ethiopian and the ordinary Guinean and not just a few elites.”
- On discrimination
“As somebody who has family in Kenya and knows the history of how the country so often is held back because women and girls are not treated fairly, I think those same values apply when it comes to different sexual orientations.”
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