3M brand, exterior grade, double-sided foam tape.
It is sold by many auto parts stores in 15 ft. rolls for permanently mounting trim or molding on vehicles. It is also available on Amazon if you can't find it locally. It comes in your choice of 1/2" or 7/8" widths. I like having both sizes around. Otherwise, I find myself cutting the thicker one in half lengthwise at times. A roll usually costs somewhere between $11 and $15.
This stuff is excellent any time you want to semi-permanently attach almost anything with a flat surface. I have never had it fail to hold things together, especially if the surfaces being attached are clean, dry, and free from oils. It can be removed with a bit of effort, but it does take some effort. Take care using it on surfaces that might be damaged if you later decide to pull them apart from one another (painted walls, wallpaper, etc. are probably weaker than the tape).
I highly recommend this stuff. It gives you an instant bond without the cure time or mess of glue. It is surprising how many uses you will find once you have it around. If you are looking for a last minute Christmas gift for someone who likes to tinker, you could do worse.
I feel like I need to throw in a disclaimer. I am not employed by 3M. I don't think I've ever met anyone who works at 3M. They aren't paying me; this is just my opinion of this product.