Wednesday’s talks will cover both security concerns and corruption - two areas the US administration says is holding back growth in Africa.
US firms have pledged $14bn (£8.3bn) in investments during the summit.
Such investment will fight extremism across the region, US Secretary of State John Kerry has told the BBC.
In an interview with BBC’s HARDtalk on Tuesday, Mr Kerry said stability from business projects was countering extremist ideologies and militant movements.
“There will be less Boko Harams, less al-Shababs. There will be less cause for people to have their minds filled with extremist ideology rather than to engage in the broader benefits of society.”
In opening remarks at the state department on Wednesday, Mr Obama said Africa was a stronger continent despite challenges it faces, including the recent outbreak of Ebola.
“A new Africa is emerging - some of the world’s fastest-growing economies and a growing middle class, the youngest and fastest growing population on Earth,” Mr Obama said.
“Africa will help shape the world like never before,” he said, adding: “Africa’s progress is being led by Africans”.
Leaders will discuss economic growth, security co-operation and improved governance in private talks during the day, ending the summit with an afternoon press conference.
Elsewhere in Washington DC, first lady Michelle Obama and former first lady Laura Bush are hosting a conference for spouses of the African leaders focused on education and health.
In an open letter in Seventeen magazine, Mrs Obama described a lack of educational opportunity for young women around the world, and urged US teenagers to not take their educational opportunities for granted.
“As you get yourself on track for higher education, I hope you’ll work to give girls around the world opportunities to attend school too,” she wrote.
The Obamas also hosted the leaders during a group dinner at the White House on Tuesday evening.
In a brief toast, Mr Obama reminisced about his family’s trips to Ghana, South Africa and to his father’s hometown in Kenya.
“I stand before you as the president of the United States and a proud American. I also stand before you as the son of a man from Africa,” Mr Obama said, adding “the bonds between our countries, our continents, are deeply personal”.
The three-day event is the first of its kind in the US, although similar summits have been held in China and Europe.
The presidents of Liberia, Guinea and Sierra Leone cancelled their plans to attend amid an Ebola outbreak, and sent delegates instead. BBC
