Can my fiance adopt my kids? How?

My ex husband told a judge in Indiana on March 31, 2010 that he wanted to sign over his rights to my 2 children. She said that he couldn't do it unless there is someone willing to adopt them. My fiancé wants to adopt them and we have been together for almost 3 years. They don't even remember their biological father and have always called my fiancé "daddy" which was their choice to do. (They asked me one day if they could call him daddy) Since it has been almost 4 years since this happened, and he still has had nothing to do with my kids, will it still be easy for him to adopt them? I will also add that the judge ordered him to continue paying child support until adoption is established, although he only pays for my son, not my daughter. We live in Missouri now (and also got the court’s permission to move out of state) and my ex still lives in Indiana. I have contact with his mother via Facebook, so he does have a way to get a hold of me to try and get in contact with my children if he wanted to. He obviously has chosen not to. I have not married my fiancé yet as we are waiting until he has completed college and has a good job, but we have all lived together for the last almost 3 years now.