This happened because Columbus “discovered” the New World, thus leading to a situation where Europeans colonized those continents and brought African slaves to work for them.
Columbus was looking for trade routes to the Orient when he discovered the New World. He felt that Asia was really not as far from Europe, going west, as most people thought. Therefore, he believed that people could get their more quickly by sailing west than by going around Africa and east. He was wrong, but he discovered the Americas. This created a connection between Europe and the Americas.
Once the Americas were discovered, Europeans started to come and colonize. Many of the Europeans did not really want to do the manual labor involved in things like agriculture on their own. Therefore, they decided to use slaves to do their work. They eventually decided that the best place to get the slaves that they needed was in West Africa. This created the connection between West Africa and the Americas.
Thus, by trying to find a trade route to the Orient, Columbus created a situation where Europe, the Americas, and West Africa were connected.