One of you will have to move out. Whoever’s on the lease stays.
If you’re the one that needs to move out, just pack your stuff and go. Then meet your ex in a public place to let them know it’s over.
If they are the one who will have to leave, ask a couple of friends or family over for support. Talk to your ex privately in another part of the residence and let them know that they need to pack up and go.