I would advice you to contact an adoption service provider in your state or a qualified adoption attorney who is familiar with the adoption laws before attempting to proceed with the process. Basically, your uncle and his wife have to petition the court to grant adoption, presenting proof that they have satisfied the essential legal elements. After an investigation, the state adoption agency will give its report on your uncle to the court which will make a recommendation. You can find more information on adoption at http://www.childadoptionlaws.com/
Initially, give them legal guardianship/custody. That is quick and will keep him out of the system. Find a paralegal to do the paperwork if there is no one in your court system that does that. It takes 6 months to a year to adopt. Legal guardianship would only take days.