Wonderful, wonderful news... as a birth parent and a step-parent, I have seen both sides and I am very happy for you... and your wife and children.
I can tell you from experience... don't count on the father letting you adopt. Custody is not the same as parental rights - he may have lost custody, but unless he has lost his parental rights, you need his approval to adopt his children. Talk to your lawyer about the difference. It will cost you, but if you can push hard on the neglect and the drugs, you may easily get his parental rights nullified, and then adopt the boys.
Blessings to both of you!