Why was Africa colonized last of the continents in the Age of Discovery?

In fact during the Age of Discovery, Africa had been the principal objective.

It really begins with Prince Henry the Navigator, a son of the King of Portugal who had an intense fascination with Africa. In particular he was taken with the legend of Prester John, said to be a descendant of one of the Three Magi who presided over a magical land with marvels such as the Fountain of Youth. Prince Henry believed Prester John's kingdom to lay in Africa, somewhere around Ethiopia. He felt if the Portuguese could find a sea route around the Muslims they could find this fantastic land. Plus, he wanted to know where the African gold was coming from, and find a way to stop pirate attacks against Portugal.

Henry's passion led him to gather together some of the leading mapmakers and to seek out innovative ship designs and navigation techniques, with the objective of developing the technology of exploration for purposes of sea travel along the West African coast. He sponsored expeditions to nearby islands and down the coast until they achieved a route around the Sahara Desert. This enabled the establishment of a mercantile trade in slaves and gold.

Building on these discoveries, the Portuguese pressed on to East Africa and eventually India, and established a strong monopoly over the trade routes they established.

Spain also wanted in on the action, but the monopolies over the African routes didn't give them many options, until Columbus and his crazy ideas came along.

Columbus was from Genoa in North Italy but since childhood had been bouncing around the Mediterranean and Atlantic on various trading expeditions, eventually getting involved in some of the West African Portuguese trading. During this time he had been self-educating with whatever books he could find. He came up with some rather novel (and wrong) ideas including a misunderstanding of the exact size of the Earth. Like so many engineering errors, it was a units error: He used the shorter Roman mile instead of the Arabic mile, resulting in a circumference of 30,200 km rather than 40,000 km. He further estimated Asia as much larger than in actuality, and believed in the existence of the mythical land of Antilla with its Seven Cities.

So, due to compounding of various misconceptions and errors, Columbus underestimated the distance from the Canaries to Japan as 3,700 km, rather than the true distance of 19,600 km (or 12,000 km if North America didn't exist). He applied to the Portuguese king, but his experts correctly rejected his estimations as too low. Plus, the Portuguese had just discovered an eastern route to Asia thanks to Bartolomeu Dias, so what did they need Columbus' far-fetched ideas. The Spanish monarchs, looking for some sort of advantage in the European trade struggles but also doubting his calculations, weren't so picky. And thus America was discovered. Fortunately Columbus understood how the Trade Winds worked or he'd have never returned.

Spain had an advantage of a surplus of experienced soldiers following the Reconquista, although many of these adventurers were organized as mercenary groups and had history been different could well have been expected to sign on with the Portuguese.

Shortly thereafter it became clear that Spain and Portugal would be fighting over the new discoveries. With the Church's help the Treaty of Tordesillas was established in 1494, essentially giving Portugal rights to Africa and Asia and parts of South America, and Spain rights to most of North America and the rest of South America.

This did enable Portugal to colonize Africa, which they attempted in Angola, Mozambique, etc. Portugal also established a ton of small trading forts and territories along their trade routes, much as Spain was attempting in the New World.

The difference was germs. In Spain's case, whereever they landed the natives would contract European diseases and begin dying off in greater and greater numbers. They failed to find the valuable trade routes they were after, but found that enslavement of the locals and colonization could return similar profits. With the European diseases depopulating the natives and primitive firearms giving a military edge, Spain found that small numbers of European colonists could dominate large amounts of land. Portugal's holdings on the other hand were filled with people not nearly as susceptible to European diseases, and while they attained rather amazing routes eastward as far as Japan, they never managed to establish strong enough colonies to displace the natives; the one exception of course being their South American colony of Brazil. The two powers continued with their differing strategies - the Portuguese building better trade relations while the Spanish expanding through conquest.

As a consequence, Portugal never really needed to colonize Africa to achieve their aims.

Later, other European powers sought to get involved. Having been left out of the Treaty of Tordesillas they simply chose to ignore it and focus on whatever lands looked ripe for the taking. Thus the Dutch, Russian, French, and British took colonies in North America, Africa, and Asia, but only in North America - with foreign disease wiping out locals - were they particularly successful.