Africa has a long history of exporting slaves going back to trading labor with Arab Caliphates. When the Portuguese acquired competent navigation technologies and gunpowder weapons, they began exerting influence in Africa's established slave trade. By the time the first Africans hit the British colonies, Brazil was already using African slaves in her sugar fields. As /u/BZH_JJM explained, perpetual servitude was not the norm at first in the early 17th century. British settlers did bring indentured servants, poor people from England who traded a set period of their life for promise of freedom and land when the contract was up. Most servants would gain independence after a set period of time. The first Africans used for tobacco farming beginning in the 1620's were usually held by similar contracts and treated the same as White servants. Race did not really exist as it does today. The colonists divided people along religious and cultural differences. Poor Europeans, Natives, and Africans could be held as indentured servants. However, unease grew as freed indentured servants posed a threat to the "old money." For example, in 1676, Nathaniel Bacon, a newcomer to Virginia from England had to settle land in the eastern part of the state as the coast already held a large population. He wanted the state to war with Indian tribes on the frontier and quarrelled with the Governor of the colony, whom he had relation to. Bacon rebelled against the governor, using indentured servants in his militia. This helped transform slavery into a racial institution, as Africans would pose less risk, not knowing the language nor geography to be competent belligerents compared to White or even Indian revolters. By the time the United States became its own entity, slavery remained restricted for Africans to their natural life as well as their childrens'.

The institution did not sit well with many. During the constitutional convention and between the 1790's and 1807, some legislators attempted to end the institution, and in 1807 importation of new African slaves became illegal, though not out of practice. With efforts from escaped slaves and whites spurred by religious awakenings, an abolitionist movement began to grow in the north that played out in various legislative compromises that hid the unease between the south and north which would eventually lead to the civil war.

edit: letters & things

The first slaves where brought to Jamestown, Virginia in 1619. Slavery was already well established in the Caribbean, on islands like Jamaica and Hispaniola. However, the primary labor source in the colony at that time was indentured servants, who took a contract in exchange for passage to America. The initial slaves where treated as indentured servants and freed after seven years. By the mid 17th century, the perpetual enslavement system was codified in Virginia, thus paving to way from slaves to replace indentured servants as the main form of labor on the tobacco plantations that served as the backbone of the economy in that period.

To add to what others have said: the way that slavery arose from indentured servitude, was that John Punch was an African indentured servant in Virginia in the mid 17th century. He tried to run away, and was sentenced to a life of indentured servitude as punishment. He was the first person who was documented as being forced into being an indentured servant for life in the American colonies. There were others who were also lifetime indentures before him, but his was the first one there are existing records for. When he ran away, he did so with 2 European indentured servants. They were sentenced to an indenture of 4 more years, indicating that the African servant received a far harsher sentence than the white servants. That was 1640.

In 1655, John Casor, also of Virginia, was declared a slave for life. He had not run away or anything of that sort--his term of indenture ended and he moved on, but was sued on the grounds that he was to be a slave for life to his master. Some consider John Punch to be the first documented slave, others John Casor. But what we see her is an evolving system of customs that made the imported African servants increasingly into property.