The reasons why Europeans turned to the African slave trade were predominantly demographic and economic in nature; the main reason was actually the shortage of labor.
When the Europeans arrived to the New World, they brought with them numerous diseases—viruses and germs that the Indigenous population didn't have any immunity against. Even the common cold was fatal to some. These diseases killed many Indigenous people, which made it easy for the Europeans to conquer new lands, but it also meant that there weren't enough people to work on those lands, especially where products like sugar and tobacco could be cultivated.
The Europeans weren't exactly familiar with agricultural work and they rarely enslaved each other, and so, in need of slave labor, they decided to turn to Africa, where the slave trade was already well-established and the African people were capable workers. The first Europeans to buy slaves from Africa were the Portuguese and the Spanish, while the British, the French, and the Dutch joined later.