"I think the fact that he is adamant probably means he was already feeling the same- it is early days, and it will get better. What you are missing is the comfort of a really supportive best friend - if you've been together at uni it is probably scary to be living alone too."
This. Honestly, you've done the right thing. The characteristics you're describing are terrific - but they would apply to any good friend. Quite naturally, you wanted sexual intimacy with your life partner. You can get the other stuff - the emotional support, the companionship etc. - from friends. Your relationship gave you everything you wanted from a friendship but lacked the physical intimacy which, for me, is key to distinguishing a partnership from a friendship. Some partners can do without it but that wasn't the case for you. As a PP said, it's one thing to sign up to a sexless relationship in your late 50s, 60s or 70s (though there are plenty who don't), but in your 20s!?!
Don't get me wrong - my DH and I are great friends and any long-term relationship should have that. But I have other great friends too. Ultimately it is the sexual intimacy - and the related emotional intimacy - that DH and I share which makes our relationship special to us. You didn't have that and you rightly recognised you needed it.
Also, the facts that he agreed with you that you should split and has been so adamant that there's no coming back from it really do suggest that, deep down, it is what he wanted also. He knew the lack of sexual intimacy was a problem, that you had needs that he was not meeting - perhaps, at some level, ending the relationship was actually a relief to him.
It's still very early days. You are only 3 weeks in. He was probably your first love. It took me the best part of a year to completely get over the ending of my nearly 3 year relationship with my first love (obviously I didn't feel awful all that time - the pain was worst in the first 3-4 months and came in waves after that). You will get over this and you will realise that this was the right decision.
Good luck, OP, and keep posting here for support.