She confirmed that Britain intends to carry over the EU's current partnership with six southern African countries - Botswana, Lesotho, Namibia, South Africa, Swaziland and Mozambique.
She also announced that the British government would invest 4 billion pounds ($5.1 billion) in African economies, without giving details.
'We're bringing ambition, pragmatism, energy and if, and I expect it will be, and if it is matched, we get a deal'.
Theresa May has signed a security pact with Nigeria's president aimed at helping the west African nation combat Boko Haram through better military training and anti-terrorist propaganda techniques developed in the UK.
May's trip is the first working visit by a British leader to South Africa since 2011.
The prime minister is also expected to visit Robben Island, where former president Nelson Mandela was imprisoned for decades, to commemorate the 100th anniversary of his birth. Only China would be ahead of Britain.
She is also set to meet with South African President Cyril Ramaphosa and hopes to visit Robben Island - where Nelson Mandela was incarcerated during the apartheid era.
May is facing pressure at home from so-called Remainers sceptical of her ability to forge trade deals once Britain severs ties with Brussels, as well as from Brexiteers fearful she will not deliver a clean break. The EU currently has an economic partnership with this union, and the United Kingdom will now continue working with it after Brexit.
The PDP urged Prime Minister May, to engage President Buhari on "the violent rigging of elections under his watch, and extract commitment from him on his administration's preparedness for a free, fair and credible general elections in 2019, especially as there are apprehensions across Nigeria, that his actions, utterances and body language suggest otherwise".
She said the comments were based on analysis first released in January that were, at the time, a "work in progress".
She conceded that no agreement with the European Union "would not be a walk in the park" and insisted that ministers are putting in place measures to ensure the government can "make a success of no deal".
Defence Secretary Gavin Williamson said: 'The danger space poses as a new front for warfare is one of my personal priorities, and it is absolutely right that we waste no time in going it alone if we need an independent satellite system to combat those emerging threats.
Brexit minister Dominic Raab said he had quickly established a "good professional and personal rapport" with the EU's chief negotiator Michel Barnier.
Her government last week outlined its preparations for a no-deal scenario.