Certain export formats enable bones to be universal to a degree. The most common export for bones/rigs is FBX. So in Blender you export your character + rig as FBX and import that FBX file into UE4 or other program.
But take exporting with a grain of salt. It's rarely perfect or thorough. For example, if you're using bone constraints on your bones in Blender, those likely won't be translated over through FBX. Mostly simple skeletal hierarchies are what exports best.