Mrs May will discuss security, trade and people trafficking with President Muhammadu Buhari before meeting victims of modern slavery in Lagos.
The prime minister already announced £4bn of extra British support for African economies during the first leg of her trip on Tuesday.
She also insisted her "sensible" Brexit plans will deliver a "good" deal.
Mrs May is travelling to Abuja, the capital of Nigeria - Britain's second largest trading partner in Africa - for talks with President Buhari.
She is expected to announce a new UK and French project to help Nigeria and Niger strengthen their borders to crack down on trafficking.
The prime minister will also pledge to support victims of modern slavery who have suffered "enormous trauma".
Speaking ahead of her visit, she said the UK was a "world leader" in trying to end modern slavery.
Labour's Shadow Home Secretary Diane Abbott said Mrs May's "warm words" rang hollow as her government had cut Border Force staff and police officers, who were "the frontline in the fight against modern slavery".
Mrs May's three-day trip to Africa is aimed at deepen economic and trade ties with growing African economies ahead of Britain leaving the EU in 2019.
Arriving in South Africa on Tuesday, Mrs May - who is accompanied by a team of business delegates - said she wanted the UK to overtake the US to become the G7's biggest investor in Africa by 2022.
She struck Britain's first post-Brexit trade pact with Mozambique and the Southern African Customs Union, made up of six African nations. The EU currently has an economic partnership with this union, and the UK will now continue working with it after Brexit.
And Mrs May also pledged a "fundamental shift" in aid spending to focus on long-term economic and security challenges rather than short-term poverty reduction.
On Thursday, she will finish her tour in Kenya, where she will hold talks with President Uhuru Kenyatta and attend a state dinner, visit a business school and meet British troops.
While in South Africa, the prime minster also faced questions from journalists on Brexit.
She told the BBC's Ben Wright that the UK is "still operating to the timetable" as it is originally set out in the Brexit negotiations.
It comes after the EU's chief negotiator Michel Barnier indicated last week that a deal may be pushed back to early November.
She played down warnings from Chancellor Philip Hammond - who said last week that a no-deal Brexit could damage the economy.
She said the comments were based on analysis first released in January that were, at the time, a "work in progress".
Mrs May then cited comments by the head of the World Trade Organisation, who said Brexit "won't be a walk in the park, but won't be end of the world either".
"We are working for a good deal, we have put forward our proposal for a good deal," she said. "I believe that deal is to the benefit, not only of the UK, but the EU.
"What the government is doing is putting in place the preparations to make sure we can make a success whatever our future relationship is with the EU and whatever the outcome of the negotiations."
Talking to journalists on board RAF Voyager on Tuesday morning, Mrs May reiterated that she believed a no-deal Brexit was still better than a bad deal.