Dear Joe:

Yes, you can have your marriage regularized once any and all impediments are resolved. Since you are both Catholic and the marriage were not in the Catholic Church, then neither marriages were valid. the fact that your previous spouses were not Catholic has no effect IF they were baptized. A marriage between validly baptized persons even if one is not Catholic is considered a valid marriage unless proven otherwise (which the annulment process seeks to determine). But in your case, since your marriages were not in the Church to begin with, the marriages would be invalid by that fact alone regardless of the religious faith of the former spouses.

You will need to check with your pastor to see if there is any paperwork needed and whatever else is needed before your marriage can be regularized in the Catholic Church.

One important thing. Since you do not have a valid marriage, you are currently living in sin. If you and your wife have been receiving the Eucharist you need to stop immediately and not receive the Eucharist again until your marriage is regularized in the Church; and you need to confess the sin of receiving the Eucharist when you were in a state of sin.

God Bless,
Bro. Ignatius Mary