She will also visit Nigeria and Kenya during the three-day trade mission.
Security will also feature on her agenda, with the threat of Boko Haram in Nigeria and elsewhere in west Africa and the work of British troops in Kenya to help countries fight al-Shabaab militants in Somalia under consideration.
People were quick to scrutinise Mrs May's quirky boogying on Twitter after footage emerged online.
At a speech in Cape Town, she will say she is "unashamed" about ensuring the United Kingdom also benefits from its aid spending.
Private sector investment is key to driving growth and "unleashing the entrepreneurial spirit" in Africa, she will say.More news: Ronaldo fails to score in Juventus comfortable 2-0 win over Lazio
As the land debate rages on, the country's ambassador to Brazil believes South Africa can learn from the South American country.
The prime minister said the government intends to carry over the EU's economic partnership agreement with Mozambique and the Southern African Customs Union (SACU), which consists of South Africa, Botswana, Lesotho, Namibia and Swaziland.
"I am unashamed about the need to ensure that our aid programme works for the UK", May will say in her speech, according to extracts released by her office.
Britain's overseas aid budget totalled £13.9 billion in 2017, an increase of £555 million in 2016 and in line with the legal commitment to invest 0.7 per cent of national income in this area.
The prime minister's trip comes a week before the huge Forum on China-Africa Cooperation in Beijing.
"We were extremely honoured to have been presented with the ship's bell of the SS Mendi", Ramaphosa said at the close of May's visit to the former British colony.
Trump said he has asked his secretary of state to look into the matter of "seizing land from white farmers".