We present an experimental study of the fully reversible assembly of oppositely charged colloidal particles in aqueous solutions. Our polystyrene colloids are charged by a grafted polyelectrolyte brush on their surface and stabilized at all salt concentrations by a neutral adsorbed polymer layer. Below a critical salt concentration oppositely charged colloids form clusters and gels with a fractal nature. The fractal dimension of those aggregates increases with increasing salt concentration. Above the critical salt concentration no aggregation takes place, due to the stabilizing neutral adsorbed polymer. Moreover, the aggregated structures are fully reversible and can be redispersed by simply increasing the salt concentration above the critical concentration. We confirm that time-dependent interaction forces are at the basis of the formation of clusters in the present system by atomic force microscopy measurements as a function of salt concentration and contact time. The force measurements show that the attraction between particles strengthens in time due to interpenetration of the polymer brushes, driven by polyelectrolyte complexation. These particles are a promising step toward a reversible and controlled self-assembling system in water, using colloidal particles as building blocks.