"I'm the first Kenyan-American to be president of the United States. That goes without saying," Obama said.
Inside a packed Nairobi gymnasium filled with nearly 5,000 cheering Kenyans, Obama offered his own personal history as evidence that all Africans have the potential to rise from even the most difficult circumstances.
"When it comes to the people of Kenya, especially the youth, I believe there is no limit to what you can achieve," Obama said. "You can build your future right here, right now."
Obama also urged nations across Africa to reject the oppression of women, likening the problem to Americans who cling to the Confederate flag, as a symbol of white power.
"Just because something is a tradition doesn't mean it's right," Obama said.
"Treating women as a second-class citizen is a bad tradition. It's holding you back," he added, condemning domestic violence, sexual assault and genital mutilation.
The president acknowledged he risked offending his Kenyan hosts when he called on the country's leaders to reject ethnic divisions and government corruption.
"I don't want everybody to get too sensitive," Obama told the crowd. "But here in Kenya it's time to change habits," Obama added, calling corruption "an anchor that weighs you down."
Recalling his family's struggles, Obama recounted how his grandfather worked as a cook for the British military. "He was referred to as a boy, even though he was a grown man," Obama said.
But the president pointed to his own family's progress from those humble beginnings.
"What these stories also tell us is about the arc of progress," Obama said. "We have to know our history so that we learn from it."
Obama also vowed the U.S. will intensify its cooperation with the Kenyan government in its ongoing battle against the terrorist group, al Shabaab.
The terror fight was a major subject of Obama's bilateral discussion with Kenyan president Uhuru Kenyatta.
"We will stand shoulder to shoulder with you in this fight against terrorism -- for as long as it takes," Obama said during Sunday's speech.
The president was introduced to the crowd by his half-sister, Auma Obama, who said her brother "continues to be very attached to us."
She relayed the story of how she picked up a young Obama at the Nairobi airport, during the future president's first trip to Kenya, in an old Volkswagen Beetle, noting that he has returned in the presidential limousine, known as "The Beast."
"He gets us," Auma Obama said. "He's one of us."
Also in the audience, along with members of Congress and U.S. business leaders, was the president's half-brother, Malik Obama, who said he was grateful his powerful sibling "finally came to Kenya" as commander-in-chief.
"This is an important step in uniting everybody and showing the whole world a true sense of brotherhood," Malik Obama said.
Although Obama did not visit his father's village of Kogelo during this visit, the president spent portions of each night in Kenya with relatives.
At a state dinner hosted by Kenya's president Saturday night, Obama described the evening as a "somewhat unusual Obama reunion."
"I suspect that some of my critics back home are suspecting that I'm back here to look for my birth certificate. That's not the case," Obama joked, before dancing and singing with the dinner's attendees.
In his speech to the Kenyan people Sunday, Obama made a concerted effort to weave his own family story into a larger narrative of hope for the African people.
"You are poised to play a bigger role in this world," the president said. "In the end, we are all a part of one tribe, the human tribe."
The president's message on female oppression resonated with Josephine Kulea, a women's rights activist who wore a radiant traditional African dress for the historic speech.
"The things he mentioned are real here and they need to be tackled," said Kulea.