By his own admission, this person doesn't have a very good track record, so what reason do you have to think the future will be any different? He says all that is behind him -- but what evidence is there to support his claim?
Yes, he knows he's been on the wrong road in life and he may sincerely want to change; many people do. But does he have the inner strength to do it? I urge you to face this question honestly, and not be swayed by your emotions. The Bible warns, "Can... the leopard (change) its spots? Neither can you do good who are accustomed to doing evil" (Jeremiah 13:23).
Only God can bring lasting change to our lives -- and regardless of what the future holds for this relationship, my prayer is that this will happen to your boyfriend as he gives his life to Jesus Christ. And if you have never committed your own life to Christ, I urge you to do so today.
The most important advice I can give you, however, is to seek God's will -- not just about this relationship, but about every detail of your life. God loves you and knows all about you, and He wants to guide you so you make right decisions about your future. Put your life into His hands, and then ask Him to guide you to the husband of His choice -- one who loves God, and will love you as well.