Congrats on getting your place minimalised 
There is a hoarding thread on here and on the Minimalism threads there are people who have spoken about it and have relatives that hold on to pretty much everything where you might get better tips than I can offer.
But based on my own experience (fortunately DH is actually better than I am, but I have relatives that hang onto everything)...
You could start by just approaching the shared space issue - taking an area like the home office, saying that you are reorganising it to make the most use of space, and how you would like to avoid clutter piles or random areas. If he is genuinely uncomfortable with throwing things out, and that is a much bigger issue than merely decluttering, then perhaps having his own dedicated space to put things out of sight so that it doesn't stress you, but not thrown out so it doesn't stress him. Like a small set of drawers, or cupboard, or nice boxes, something you'd feel fine looking at but that would accommodate his things for now.
Obviously you can't just keep buying furniture to fill with old receipts and things, but it might be a start for helping you to enjoy your living space too just like you can handle your bedroom for now as it's out of sight.
Then perhaps you can start to broach the real issue - I don't have enough experience to say whether someone has a genuine problem or how to handle it if they do - however there needs to be a balance between him feeling comfortable at home and you also feeling comfortable.
I have a close relative that struggles to get rid of things and is very focused on what might be useful later, even things they have had for 10 or 20+ years and never used during that time. They can actually give things away, or chuck out old things, the problem is that they want to go through every single item to make sure that it is indeed rubbish or give things to people/charities when it may not be anything people really want (eg really old toaster, but still functioning). However they don't have a full-on hoarding house/problem to the extreme that you might see on documentaries, everything gets stuffed into wardrobes, attic space and so on. Maybe your DP has a way to get rid of things, like going through things one by one, or giving to charity to know it will be useful to someone else. Also small steps, like considering going through a few bits in his wardrobe, or a bedside cabinet, and taking it from there. Slow and steady would be much better progress than doing nothing or having an argument over trying to go too fast.
But, if he does not struggle that much, then maybe he would let you organise his things and throw out the obviously useless things, like the old receipts and tat, especially in your shared space. I don't want to make any assumptions as to the extent that you've discussed this together but if you haven't then you can possibly provide a number of different possible options according to how you think it might go down/how receptive he would be, and take it from there.