Usually the Berlin conference of 1884 is cited as the main cause. Here European colonising nations basically carved up Africa amongst them to prevent them from going to war with one another over territories there. This period is also denoted as the scramble for Africa.

More interesting is the question why during the decolonisation wave 1945-1960/70 these borders were not disputed:

• by this time the culture of the colonising nation has had its impact on the colonies elite layer. Think language etc. The regimes established there basically took over the existing colonial regimes, and established oligarchic, single party states for the most part.

• there were some voices for Pan-Africanism. Calling for borders to be abolished and the formation of a African federation. A notable proponent of this movement is Kwame Nkrumah, the president of Ghana just after its independence. This movement failed for a multitude of reasons: firstly there were some states, like Ethiopia, that managed to retain their sovereignty throughout (though they were a minority) Or became ruled by a white minority's government in the wake of decolonisation (South Africa for example) Secondly due to the nature of the oligarchic regimes in most countries, the leaders were not eager to give away their newly won independence and power. Thirdly, and the thing that killed off border redrawing most definitely, was the treaty signed by the Organisation of African Unity members in 1964, which stated that the borders as defined upon reaching independence by a nation would be respected.

Sources:

R.R. Palmer et.al. A history of Europe in the modern world

A. Best et al, International history of the 20th century and beyond.