Li is scheduled to visit Ethiopia, Nigeria, Angola and Kenya during the trip, which begins Sunday and lasts for a week, officials said. It also includes a visit to the headquarters of the African Union in the Ethiopian capital Addis Ababa.
The trip follows one Chinese President Xi Jinping made to the continent last year, shortly after taking office, a journey that underscored Africa's importance to China, the world's second-largest economy.
China's economic growth has been partially fuelled by African natural resources, including oil.
"It is an important visit oriented towards the whole continent," Zhang Ming, Chinese vice-minister for foreign affairs, told reporters, stressing that Li will be visiting Africa's eastern, western and southern regions.
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It "highlights the great importance we attach to China-Africa relations", he added.
Zhang also said that renewing the "traditional friendship" between China and Africa as well as advancing a "new type of strategic partnership" were goals of the visit.
Li is scheduled to spend three days in Nigeria, where he will meet President Goodluck Jonathan and also attend the World Economic Forum on Africa, which starts in the capital, Abuja, on Wednesday.
The foreign ministry said six major agreements would be signed during the three-day trip, including "economic and technical cooperation", aviation, banking and health projects to combat malaria.