I answered this in part earlier

The enslavement of Africans was the result of the convergence of multiple factors. The first factor was the cut off of the slave trade from the east when Constantinople fell in 1453. Originally, Slavic and the people of the Caucuses provided the slave labor for the peoples of the Mediterranean.

The fall of Constantinople also complicated the spice trade because the trade routes were now controlled by the Ottoman Empire. In an effort to find a way around the Ottomans, the Portuguese and Spanish began to send expeditions to try to find new sea routes to the east. Along the way the Portuguese and Spanish conquered the islands of the Atlantic right off the African coast and set up forts on the African coast itself in order to trade with the Africans and resupply their ships. The trade originally centered around the gold at first and slaves were a secondary factor.

At the same time the cultivation of sugar had spread west to Spain and Portugal. Europe's sugar addiction was beginning and the Spanish and Portuguese saw a chance to cash in. The islands off of Africa were a perfect place to grow sugar because the climate was right. The problem was that sugar was a very labor intensive product. The Spanish and Portuguese tapped into the trading networks they had been using to get gold and instead got slaves. These slaves worked on plantations on the islands off of Africa and began to make a substantial profit.

At the same time the New World was "discovered" and the Spanish and Portuguese needed labor to extract the riches of the New World. They turned to the Native population but the Natives began to die off in large numbers due to disease or were running away. To replace them, the Spanish and Portuguese did what they did on their islands in Atlantic and applied it to the New World.

By the 17th Century the British were beginning to control the seas and seize islands in the Caribbean as well as colonize what would become the United States. In the Chesapeake region, tobacco was planted and exported. At first, the tobacco plantations were worked by white indentured servants but they worked under brutal conditions. Eventually word got back to England that the conditions on the plantations were not worth the pay and land. Therefore, African slaves were brought in to do the work that indentured servants were no longer willing to do.

Inhuman Bondage by David Brion Davis has a great chapter about this very subject.

Chattel slavery or indentured servitude?

The first documented slave for life in Colonial America was John Punch, who was brought over from Africa as an indentured servant. He ran away, was recaptured, then was sentenced in 1640 to lifetime servitude.