We study fractal vesicle aggregates whose morphology is conditioned by the interaction between the lipid vesicle membranes and calcium and magnesium ions. These morphologies are probed by means of static light scattering using a cross-correlation scheme that avoids the multiple intracluster scattering. In contrast to the branched structures induced by calcium, we report a singular surface- to mass-fractal transition controlled by the magnesium concentration. From infrared spectroscopy data we conclude that the specific dehydration of the lipid membranes due to these cations plays an essential role in short-range intervesicle interactions.