Getting full custody is different than having a parent's rights terminated. If the biological mothers rights were never terminated by the courts than she may still block the adoption. If her rights were in fact legally terminated than you need to call a lawyer and he can give you the details on what you will need to have in order to complete the adoption.
If the biological mom's rights were not terminated, but she has not had contact with the child in over 6 months to a year (depending on where you live) then you can file for a TPR (termination of parental rights) and then for an adoption. This will take longer, but the end result will be the same.
Kuddos to you for sticking it out and staying in your stepsons life through thick and thin, it takes a very strong and loving person to do so.
Stepparent Adoption Blog