The US first lady will also visit the Hector Peterson Memorial to the young boy killed in Soweto's 1976 anti-apartheid protests.
"I am doing this because we know that Africa is a fundamental part of our interconnected world and when it comes to meeting the challenges of our times,” she said before setting off.
“Whether it is climate change or extremism, poverty or disease, the world is looking to African nations as vital partners and will be looking across the continent to young people just like all of you to help lead the way," she added.
She will also be the key speaker at a conference of the Young African Women Leaders Forum − a two-day meeting of 75 women aged 16 to 30 who act as community leaders across the continent.
Her visit is a mix of policy and also a personal pilgrimage, said the US State Department. "She's coming on this trip to talk about women's development and youth development, and South Africa's a leader in that, not only on the continent but globally," said Elizabeth Trudeau, spokesman for the US embassy in South Africa’s capital, Pretoria.
"A visit to South Africa is important for them as a family. She'll be visiting many struggle-era landmarks."
On Thursday she will host disadvantaged students at the University of Cape Town, before meeting groups that work to stem HIV/Aids in South Africa, by using football to reach out to children with information about the virus.
There will be a meeting with Archbishop Desmond Tutu, Nobel Peace Prize laureate and a key figure in the struggle against apartheid and in later helping South Africa overcome its past.
She heads to Botswana on Friday to meet President Ian Khama in the capital, Gaborone, and visit a clinic that teachers teenagers about leadership and HIV/Aids.
White House officials said her visit would boost her husband's foreign policy goals.
"This trip by the first lady is very directly connected to the president's agenda in Africa and the Obama administration's foreign policy in Africa," said Ben Rhodes, President Obama's deputy national security adviser.
"It's no coincidence that she would be visiting countries that have embraced democracy, (and) in many respects, have shown that not only does their democracy deliver for its citizens, but it can provide a positive example for the neighbourhood that these countries are in as well."