Yes, you should tell him, but it needs sensitivity, so you need to think about the timing. It will come out sometime, so better to do it well.
I found out I had a half-sister when I was 26; I had had absolutely no idea, and it totally turned my world upside down, and I still have trust issues (now in my 40s) - what else might they have lied about or just not told me? My full sister had had some inkling that there was some unknown history, but had actively decided not to find out, and was really angry with me for making her know - but I hadn't known she'd decided not to know (we'd never talked about it, and I was too naive to have had any suspicions that she had.) And in any case, it's an impossible situation - if she later found out that I knew and had decided not to tell her, then she'd have been angry about that, too, and it wasn't fair on me to carry the burden of knowledge alone.
How your husband reacts will depend on a whole host of things, including any suspicions he may already have had, what his relationship is like with his father, whether he has any full siblings. Does your FiL have contact with his earlier family? Would there be chances of meeting up, if anyone wanted it?
I think I'd probably want to tell him myself, but I might want to talk to FiL first, but that also depends on how you get on with FiL. It might be better coming from FiL - as I say a lot does depend on existing relationships, and this is going to change them irrevocably. Things won't ever be the same again, but it should come out, in a way you can control, rather than being blurted out in the heat of an argument sometime or something like that.
I hope for all your sakes it helps to make your lives better. If not - well, I saw a therapist, and that helped. Good luck.