It sounds like you're going to feel like crap until you tell him the truth.
It's not really you he's best friends with, it's partly you and partly the made-up person you presented. It's kind of like catfishing. He didn't get the choice to become friends with you, he got the choice to become friends with someone who doesn't exist. Had you told him the truth, he may have chosen to pursue the friendship and he may not have, but he wasn't given the opportunity to give informed consent. If you feel true friendship toward him, then you're going to need to give him that opportunity.
Realistically, rationally, you're probably going to lose the friendship. If he didn't lie as well, then he's made himself vulnerable to you as the person he thought you were, and he's likely going to feel betrayed as well as other things, and want to protect himself from further harm. I can't speak for him of course. If I were in the same position, I would feel betrayed and upset at how much I'd disclosed in trusting and being vulnerable.
If you lose him, you're going to hurt, but you can also gain self-respect for having done the right thing, and learn from the experience for going forward. It's a difficult lesson in becoming aware of how what we do affects others. People go through difficult lessons in life, but making mistakes is how we learn. You're hardly the first person who's been thoughtless and had to experience consequences and learn from it. That's just being human. If you act in integrity toward him now, then you begin to build a foundation for integrity and it will get easier to maintain it.
I think if you tell him it's best to give him the space to do as he sees fit and to not push him. Once you disclose, it's not about you anymore. Since the friendship was built on a false foundation, there's probably not going to be a frienship anymore. If he's okay with it, I have to wonder about his self-respect, and/or if he has a romantic or interest in you that he himself was not disclosing.
I don't mean to be harsh with you, just direct and honest. I commend you for speaking up and asking for input. I hope you can see that I have compassion for you, for what you did, and for the situation that you're in. I didn't throw any blame at you. In such situations, I respond the same as I would with a good friend and tell the truth. The truth may hurt, but it never harms. Remaining in error and ignorance is what harms, and it seems to me you're releasing both.
