There was a listing on here once where the person glued the completed puzzle to cardboard and then framed it like a picture and hung it on the wall if that helps.
That really depends on what you ultimately want to do with it. If you just want to keep it all together, you can apply watered down 40/60, 40 water and 60 wood glue (or modpodge, I think it's called) to the back. you could also apply a non yellowing, water based sealer to the front. For a more permanent fix, you could glue it to a piece of hardboard (masonite), supaboard, or plywood. you could also have it framed.
Hope this helps.
I use ModPodge on the back first, I put 2 coats and then put a poster board on it. Let that dry, flip it over and do the same on the front also using 2 coats. Then if you want to you can leave a border of the poster board for accent or trim to fit. I haven't had the ModPodge yellow on me.
I have also done polyurethane on the front. I use 2 to 3 coats.
Have fun with it.
They make a glue just for that purpose.