This is a pretty easy repair, but we need to ask, why is it loose? What has failed?
It is entirely possible that the brace was lacking glue in that area, and has come loose. But it is also possible that there was a bad batch of glue used, or the brace is warping badly, which means you might want to reconsider gluing it back in place, as it could warp the top. Also, it could have come loose because of some other failure.
Reach in and hold the brace in place. What happens? Does it take a lot of pressure, or just a tiny bit? Does it warp the top to hold it in place? Does it pop off the rest of the way and fall into the instrument?
And, most importantly, is anything else loose?
We don't know what kind of glue was used here, which also complicates things a bit, but not badly.
I would do the following -
Glue some 120 (or so) grit to an old gift card or other thin, stiff backer. Cut this into a section that you can work with, and use it to do just a little sanding in the gap. This will clean up some of the old glue.
Get some blue tape, and place it on either side of the brace, to keep glue from spreading everywhere. I would also cut out a sheet of paper that will fit inside of the uke and cover the back of the uke from glue drips.
Work some glue into the joint, and then clamp it shut. I would put a flat piece of wood or acrylic on the face of the uke to protect the top, and use a small c-clamp without much pressure (very little, it doesn't take much) to hold it in place. Let dry for 24 hours.
As far as glue goes, you would be pretty safe to glue it with regular Titebond wood glue.