The US president was greeted at Addis Ababa's international airport by Ethiopian Prime Minister Hailemariam Desalegn.
On Monday, Mr Obama is due to discuss ways to bring South Sudan's 19-month-old civil war to an end.
At the scene: Karen Allen, BBC News, Addis Ababa
Compared to the Kenyan leg of his tour, President Obama's arrival in Ethiopia signals a more sombre mood.
Ethiopia is a close ally of the US in fighting militant Islamists. Thousands of Ethiopian troops are in Somalia, where the capital Mogadishu was the scene of a major bomb blast on Sunday.
But despite security ties, Mr Obama is expected to raise concerns about what critics say is the erosion of democratic freedoms in Ethiopia.
Recent elections in which the ruling party secured all of the parliamentary seats, and a further clampdown on the media and the jailing of bloggers, are among the issues on which the US president is expected to express alarm.
In talks with leaders from Ethiopia, Kenya and Uganda as well as the Sudanese foreign minister, he is expected to call for tougher sanctions and a possible arms embargo if the warring factions do not agree on a peace deal.
However, a US official travelling with Mr Obama said Monday's talks were not expected to lead to a breakthrough.
"This is an opportunity to reinforce the effort that's on the table and to strategise... on next steps in the event that it doesn't succeed," the official told reporters.
Fighting in South Sudan has left thousands of people dead and displaced more than two million.
Security issues will also be on Mr Obama's agenda as Ethiopia, like Kenya, is battling the jihadist group al-Shabab.
Correspondents say he is also likely to call for greater democracy and human rights while in the country.
Ethiopia's ruling party, the EPRDF, and its allies won every single parliamentary seat in May's elections. Opposition parties claimed the process was rigged.
Some rights groups have criticised Mr Obama's visit to Ethiopia, warning that the trip could lend credibility to a government accused of jailing journalists and critics.
Amnesty International's Abdullahi Halakhe said: "We don't want this visit to be used to sanitise an administration that has been known to violate human rights."
Human Rights Watch and other organisations urged Mr Obama to put the "pressing human rights concerns... at the forefront of your discussions".
A legal case currently being fought through the US courts alleges that agents of the Ethiopian government eavesdropped on the internet activities of a man in the US state of Maryland.
The man, born in Ethiopia and now a US citizen, works for a political opposition group outlawed in his home country.