My finace and I have 2 babies together. He wants to adopt my older 2 children. The bio father signed over his rights years ago and the court gave me sole custody. Do I have to be married in the state of TN for my fiancé to adopt?

While I do not wish to disagree, I doubt he "signed over his rights" since that really is not possible. He may have signed to give you sole custody, and he signed that he did not wish visitation at that time.

You will need an attorney to look over the paper work, but I would really bet, that he never signed over all rights. And you will still have to get him to sign to allow the adoption.

And yes TN does require marriage for about one year prior to adoption.

Just because you have sole custody does not necessarily mean he "signed over his rights." Sole custody simply means that you have custody of the children. By signing "over his rights" he would have no right in making decisions when it comes to the health and wellbeing of the children involved.

In the state of Tennessee, your fiancé cannot adopt. You must be married for a period of no less than six months to a year, with consent of the biological father, for an adoption to be approved by a court of law.

The court looks at it this way...

If he is not committed enough to you to be your husband, he won't be committed enough to take on the role of permanent father.

As has been said you first have to be married. However, this is a perfect time to start looking around at family law attorneys because you will need one to prepare the adoption papers. That way when you have been married long enough things will be in order.
Do you have an order for child support? I ask because sometimes (not always) knowing that they will no longer have to pay child support will push the ncp in the direction of allowing an adoption.

... The court looks at it this way...

If he is not committed enough to you to be your husband, he won't be committed enough to take on the role of permanent father.

Which brings up the question: you have two children together but yet you have not "tied the knot". Why not (no pun intended)?

You have been in a relationship for at least 9 months (or 18, unless they are twins). Isn't that long enough for him to be just a "fiancé"?