This question is targeted before the Constitution.
Depends a lot on the time and location, but slaves were typically prisoners of war.
For the American colonies, there was considerable debate in the beginning over whether black slaves could be considered "indentured," whether slavery could be inherited, and whether baptism rendered a man unfit for slavery. The colonies ended up passing "black codes" that codified African-American slavery into the form seen until the Civil War.
Initially, blacks were brought in under the same indentured servitude agreements as whites. It wasn't until a black man sued to keep his African servant for life that slavery of blacks became for life.