Look for clear epoxies, sometimes sold for encapsulating. They'll stick fairly well to both materials, though presumably not as well as epoxy sold as glue. You have a lot of contact area so the bond will be strong anyway. A two part epoxy should be quite cheap - if you can get an appropriate size pack, and I'd expect curing over a few hours though you might be able to get quicker.
To have it as clear as possible, you need to make sure that you apply enough to fill the gap and get all the air out.
I've bonded two sheets of clear plastic (one acrylic, one unknown) using ordinary glue epoxy (i.e. not meant to be transparent). That was good but not good enough for your needs. It was very slightly milky, and it cured before I had time to make a jig that would apply enough so I had a few bubbles.
It is possible to sand and even polish (with fine wet-or-dry paper) cured epoxy, so it could be used to seal the edges as well. This might be too much work though.