There are two types of dependents, a "qualifying child" dependent is eligible for up to a $2000 credit, and "qualifying relative" dependent for a $500 credit.
To be a qualifying child dependent, the child must be a close blood relative, or have been placed in your home by the state government or by a foster placement agency that operates with government approval. A voluntary placement does not count. Close blood relative means a child of your parents (your sibling or half-sibling), a child of your brother or sister (niece or nephew), or a descendant of one of these (grand-niece, etc.)
If the child is not your qualifying child dependent, they can be your qualifying relative dependent if they have lived in your home since they were born, you pay more than half their expenses, and there is no biological parent who has a priority claim (it sounds like there is not, if the child never lived with either biological parent).
Also, the child must have a valid social security number that is issued before the due date of the tax return, including valid extensions. If you don't have an SSN, wait to file until you get it, even if it means waiting after the April 15 deadline (but be sure to apply for an extension if you have to wait that long.)