"On behalf of our family we're deeply humbled to stand where men of such courage faced down injustice and refused to yield," Obama wrote in a message in the visitors book co-signed by his wife Michelle.
"The world is grateful for the heroes of Robben Island, who remind us that no shackles or cells can match the strength of the human spirit."
Obama's visit to Robben Island came as Mandela entered a third week in hospital 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 Sunday began with a flight to Cape Town and then a helicopter ride to the museum on Robben Island. He said he was eager to teach his children 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.
On Saturday he told reporters that 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 honor."
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 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. – Sapa-AP