Glue for leather parts
There are specialist leather glues available that are ideal for this application (on Amazon, for example), but if you don't want to buy glue just for one small join then ordinary contact adhesive will do a good job. Epoxy resin will also join the leather, but is less flexible. 

Many people also swear by Barge cement, but I've not used either so can't really comment as to their effectiveness.

Avoid superglue and PVA, which will both do a poor job of sticking the leather together and will make it brittle (superglue moreso than PVA).

However, bear in mind that gluing is normally not as strong as stitching or riveting; if you expect the join to be under any kind of tension I would recommend that you stitch or rivet it instead. (thanks to Matt for reminding me of this)

Sources: experience, here, here and here