Here we report the shape transformation of poly(ethylene glycol)-polystyrene (PEG-PS) polymersomes into ordered inverse morphologies, directed by the salt concentration of the medium and the presence of azide groups on the polymersome surface. The azide moieties introduced at the chain ends of the PEG blocks induce a difference in hydrodynamic volume of the hydrophilic domains at the inner and outer side of the vesicular membrane, allowing control over its spontaneous curvature and hence the pathway of shape deformation. This simple modification enables access to intricate morphologies which are traditionally only accessible via the application of complex polymer building blocks.