The US president will also visit Tanzania, Ghana, Liberia and Rwanda during his tour.
The tour is likely to be Bush's last visit to Africa as president.
He has a high approval rating on the continent after initiating the largest emergency HIV/Aids project in history. He is now aiming to raise this $15bn fund to $30bn.
Bush said his message was "that the American people are a compassionate people, a decent people, who want to help moms with - deal with malaria, and families deal with HIV/Aids, and the need to feed the hungry."
Laura Bush, the president's wife, will also be on the trip. It is her fifth visit to Africa and her husband’s second.
Military and oil
The conflicts in Darfur and Kenya will also be on the agenda. The tour will expectedly witness lobbying by African leaders on where to locate the new Africa Command headquarters – called Africom.
US military command for Africa, created a year ago, is currently in Stuttgart, Germany.
Liberia has offered to host the headquarters, whereas other African nations have expressed concern over the level of influence it would give the US in Africa.
Bush said: "Africom is a brand new concept aimed at strengthening nations' capacities to deal with trafficking or terror, but also to help nations develop forces capable of doing the peacekeeping that unfortunately too often is needed on the continent."
Oil interests are also expected to be discussed.
The US expects that one-quarter of its oil imports will come from Africa by 2015.
Talking of America’s African foreign policy on Thursday, Bush said: "I couldn't live with myself if I didn't develop an effective strategy and call upon the American people to help."
He also said that the relief of poverty in Africa would help counter the rise of terrorism: "If there's hopelessness, they have a better chance to recruit."
However, critics have already said that the tour neglects troubled areas, such as Sudan and Kenya. Even before Bush landed, protests against his visit took place in Tanzania and Rwanda.
Hundreds of Tanzanian Muslims demonstrated in Dar Es Salam.
Rwandan Hutus say that Bush's visit is an endorsement of Paul Kagama, the Tutsi president whom they call "bloodthirsty".
Bush is sending Condoleeza Rice, the US secretary of state, to Kenya during the trip.
She will arrive in the capital Nairobi on Monday and has been trusted to give the message that democracy must be reinstated.
Bush said there was a path forward in Kenya, which has been engulfed in violence after a disputed election in December.
"There is a way forward, which is for the parties to come together in good faith, and work out a way forward until there are new elections."