In terms of justification, white Europeans used the Bible to vindicate African slavery. Located primarily in the Old Testament (Genesis 6-11) Biblical scholars zoomed in on what is called "The Curse of Ham" simply put, after the Great Flood, Noah gets drunk on wine and passes out in his tent, one of his sons Ham, sees his nakedness and tells his brothers, Shem and Japheth. When Noah awakens he is outraged and curses Ham.

“Cursed be Canaan! The lowest of slaves will he be to his brothers.” He also said,“Praise be to the Lord, the God of Shem! May Canaan be the slave of Shem. May God extend Japheth’s territory;may Japheth live in the tents of Shem, and may Canaan be the slave of Japheth.

In this passage Canaan/Ham (The African) is cursed to be the slave of Shem (The Asiatic) and Japheth (The Caucasian). As time went on, the black race was barbarized further by the inclusion of the Tower of Babel to their racial history in which the character Nimrod (grandson of Ham) is blamed for the confusion of the tongues and Gods further separation of the races on the Earth. So by using Biblical justification, they dehumanize the African race and thus make it easier for slavers to morally condone slavery.

As for the physical aspect, when the Europeans first arrived in the Americas, Native American slaves were used quite prolifically, to the point that many of the tribes were wiped out. In order to keep up the work force, African slaves were brought in by an already existing slave trade created and utilized by the Portuguese, Genoese, and Spanish. The British first broke onto the scene in the 1550's when Admiral John Hawkins raided slave ships and sold their cargo in the New World

Sources: Noah's Curse: The Biblical Justification of American Slavery, Stephen Haynes A History of Latin America Benjamin Keen, Keith Haynes

In addition, many of the Biblical arguments used to justify slavery were used to justify American segregation as well, see this 1955 pamphlet God, The Original Segregationist