I don't think I can work with this person anymore. How can I change my circumstances to avoid continued working with this individually in a professional manner?
If you want to avoid working with this person one option could be to quit and find a new job. However, that does not shield you from finding that in your new job someone else was convicted and also did his time, so this does not seem to be a good solution in the long run; you probably don't want to quit every time you find out someone has a criminal record.
Another solution is to ask your boss to assign you different tasks than the ones your coworker does, explaining him you have personal motives to wish so. However, this does not guarantee you that your boss will agree and separate you from this coworker. Probably you will have to provide good reasons for wanting that and not just personal ones, so your demand has more validity.
Last but not least, you can ask your coworker what are his thought about his past conviction, so you can try understand him better and change your way of thinking of him. It could be the case that he was wrongly convicted (Judicial systems are not perfect), and you are judging him without actually knowing his side of the story.
This could be a better solution in the long run, improving your tolerance towards others and learning to judge others by "walking with their shoes". Just remember to take of your shoes before trying to empathize with others.
If he was convicted and already did his time then that should have been enough punishments for your actions. Who are you to decide if someone deserves or not more punishment? That is why there are judicial systems and laws all around the world, so people don't just decide on their own someone deserves punishment and start taking actions.
Besides, most recruiters ask for criminal records of their prospect employees, so it is highly probable they already know this and still decided to give him the job.
As I commented on your post, exposing this knowledge is not only controversial and probably immoral but can also come back and affect you. I suggest you don't do it and carry on, after all he did his time already.