I'm a clean(-ish) person and my partner a messy and hoarder(-ish) person. We've been living together for a year and a half. Things aren't perfect yet, but we're getting there; it's a process. I was also a messy person until I was 25 years old, so I have an idea of what's it like on the other side. Here are a few things I learned :
You can't change someone else
I really recognize my old self and my partner in the description you give of your partner and what he thinks about his "messy" house. In this case : you can't make your partner care about the mess like you do, and clean the mess like you do. Even with the best intentions, right now your partner doesn't care about the mess, and probably doesn't even see the mess. Hoping to change that will only bring heartbreak. Let go of this idea. In time, he might change his perspective and be more like you, but it will take time, and it won't happen with you uttering a magical phrase or forcing him to. So accept the fact that your partner is a messy person and will not keep the house to your standards, even if he tries really hard.
It doesn't mean that you're stuck doing all the work, though.
Know what's important to you
Try to find out what you need to be happy in your own home. Not your ideal, but the minimum. For me, an example is I truly hate to have clutter in the kitchen. I'd love for the whole house to be clutter free all the time, but I can handle it being a little cluttered, except for the kitchen.
Being clean and organized is important to you, not your boyfriend. He should help out, it's his home too, but your partner won't be able to keep things clean and organized to your standard. So lower them. Have the lowest bar possible where if he helps out with that stuff, you'll be satisfied. Having also a concrete list will help your partner : even if he wants to help, he won't know what to do if you just ask things to be clean and organized. He'll need concrete chores to work on.
Set up a plan together
Once you know what is the minimum, have a discussion about how you'll take care of your home together. Acknowledge that you two are different, that you don't expect him to be as organized as you, but you need to find a middle ground so that you're able to feel at home with him without becoming the housekeeper. That you know that some of these things are not important to him, but they're important to you, and you'd like his help.
This should be a conversation, not you lecturing him. The goal is to find a way to make it work, and for this you'll need his input. Find a compromise. For example, you say you clean up a bit every day, which he does not. So you could leave the things that need to be done weekly to him (cleaning floors, laundry,...) and you take care of the everyday stuff. Or maybe he has chores he'd like doing better than others, and you can leave those to him.
Also, be ready to be flexible, and to have this discussion a couple of times again down the road. Your standard might change, he'll maybe have his own standards you're not respecting, the division of chores might not work... Don't be afraid to tweak things and talk to each other if things aren't working out.
Accept he will do it his way
My partner is in charge of the laundry. It takes him three days. Three. Freaking. Days. Seriously ? But the laundry is made once a week like I asked (I have a small wardrobe, so I'm quickly out of clothes), and every week-end I have clean clothes to wear for the week, so I let it go.
He won't take care of the house like you do. He won't become proactive by magic, nor should he. He is allowed to have his own system. If something is his responsibility, let him take care of it as he wishes (unless it impacts you in a concrete way, like no clean pants for the work week). You telling him he's doing something wrong just because he won't do it your way will only frustrate him and less likely to do this chore again. You don't want to hear "Well if you do it so much better, you do it !"
You'll have to (probably) remind him
I know you say you don't want to feel like you police him, but it will probably happen. At least in the beginning, because it is new to him, he won't think about it. So when reminding him, don't sound frustrated, or blame him. Hopefully you'll find a system where he'll pick on things soon.
Or not. Mine didn't. He has a list of chores that are his, but he tends to forget about them. But if I tell him in the morning "Could you clean up the kitchen today ?", he'll do it. We now have a what's app group where we give each other chores that need to be done today or tomorrow. 90% of the stuff I ask are things that he ideally "should be" doing on his own, so it's a bit frustrating, but it is what works best. I prefer to remind him to clean the kitchen than to come home and get mad. That's our system, I see it as setting us up for success. There are other tools that you could use to limit having to police him, like a chore chart, an excel file, or an app.
There are now some things that he does without prompting him, because they have become a habit. And he knows that ideally I'd like not to be the manager of the house, giving out tasks, so he's working on it. But he still needs help, and being mad at him won't change things.
Don't forget to be grateful
I say thank you when he does something I asked him to do, even if it was something he was supposed to do. I'm even more grateful when he does something extra. I know that if I weren't here, he wouldn't do half these things, it requires some effort for him, and telling him I'm grateful for his housework is important to me. He thanks me too, by the way.
It's also a positive reinforcement. If you only comment on his chores when he misses something, the chores themselves will be associated with guilt, fights, disappointment... While thanking the other person will have the opposite effect. I'd rather my partner cleans up because he's happy to help me, not because he doesn't want to be yelled at.
You'll also have quirks that will drive him nuts
I leave my shoes near the door. He hates that. I'm still working on it. That's why you need to have a conversation, not just you telling him what he needs to do.
It will be a process. We've had a big discussion about chores and house keeping before moving in, and it didn't solve everything. It took me a while to let go of this ideal I had, that our place will never be like my old place; to understand that he wants to help, but he has his limitations and let go of this ideal housemate I wanted to have. We learned to work together so that we would both like to live together in the same space.