Obama's visit to Robben Island comes as Mandela is hospitalised for a third week in critical condition. Obama was near Mandela's Pretoria hospital on Saturday, but did not see him due to the family's wishes and instead met privately with Mandela's relatives.
His schedule on Sunday begins with a flight to Cape Town and then a helicopter ride to the museum on Robben Island.
Obama visited when he was a senator but this time is bringing his family. He said he's eager to teach them about Mandela's role in overcoming white racist rule, first as an activist and later as a president who forged a unity government with his former captors.
He told reporters on Saturday he wants to "help them to understand not only how those lessons apply to their own lives but also to their responsibilities in the future as citizens of the world, that's a great privilege and a great honour".
Obama, who has spoken movingly about Mandela throughout his trip to Africa, praised the former South African president's "moral courage" during remarks from the grand Union Buildings where Mandela was inaugurated as his nation's first black president.
"We as leaders occupy these spaces temporarily and we don't get so deluded that we think the fate of our country doesn't depend on how long we stay in office," Obama said during a news conference with South African President Jacob Zuma.
Obama's ascent to the White House has drawn inevitable comparisons to Mandela. Both are their nations' first black presidents, symbols of racial barrier breaking and winners of the Nobel Peace Prize. And Obama attended his first political rally while a 19-year-old college student protesting apartheid.
Zuma said Obama and Mandela "both carry the dreams of millions of people in Africa and in the Diaspora who were previously oppressed".
Mandela's legacy also will be a prominent theme throughout Obama's speech later Sunday at the University of Cape Town, said White House deputy national security adviser Ben Rhodes. The president will emphasis "the ability for societies to change," Rhodes said, along with the need for democratic development and empowering young people.
'Up to the leaders in Africa'
Rhodes said Mandela's vision was always going to feature prominently in the speech given that the address will follow Obama's visit to Robben Island, the prison where Mandela was confined for 18 years. But the former South African leader's deteriorating health "certainly puts a finer point on just how much we can't take for granted what Nelson Mandela did."
Obama is also expected to emphasise how Mandela's democratic vision is hardly complete. While there has been progress here that "nobody could have possibly imagined," Rhodes said, millions of people on the continent still live in poverty and governments still struggle with corruption.
Harkening back to a prominent theme from his speech in Ghana in 2009, Obama will emphasise that Africans must take much of the responsibility for finishing the work started by Mandela and his contemporaries.
"The progress that Africa has made opens new doors, but frankly, it's up to the leaders in Africa and particularly young people to make sure that they're walking through those doors of opportunity," Rhodes said.
Obama will speak at the University of Cape Town nearly 50 years after Robert F Kennedy delivered his famous "Ripple of Hope" speech from the school. Kennedy spoke in Cape Town two years after Mandela was sentenced to life in prison.