Here is another way that works similarly. The solution is more complex, but it still does what it seems you want.
I know I'm late, but I still want to answer this.
Select your UV sphere and press Shift + S -> Cursor to Selected. Using Shift + A add a Curve -> Circle. Scale this up so it is slightly larger than the UV sphere, than rotate it on whatever axis: In my case, I used R > Y > 90. Now select your mesh, the person in this case. Under the Properties panel, Modifiers tab, add a Curve modifier.
Select the eyedropper in the Object data field, then click the new circle.
Make sure your cursor is still in the center of the UV sphere. Press Shift + S -> Selection to Cursor.
Now it seems the mesh is upside-down on the back. This can be fixed by mirroring the mesh with Ctrl (⌘ on mac) + M -> then Z to mirror it across the Z axis. Now he is rightside up! You can now Apply the curve modifier (to the mesh being 'wrapped') and delete the circle.
Here is my final result:
You can now parent the 'wrapped' mesh to the UV sphere. Select the person, then Shift + Right click the UV sphere. Press Ctrl + P > (Set parent to) Object. Now whenever you move the sphere, the person will follow in the same place. This is especially good for rotating it.