Magnetotelluric and seismic data, collected during the MELT experiment at the southern East Pacific Rise, constrain the distribution of melt beneath this mid-ocean-ridge spreading centre and also the evolution of the oceanic lithosphere during its early cooling history. Here we focus on structures imaged at distances approximately 100 to 350 km east of the ridge crest, corresponding to seafloor ages of approximately 1.3 to 4.5 million years (Myr), where the seismic and electrical conductivity structure is nearly constant and independent of age. Beginning at a depth of about 60 km, we image a large increase in electrical conductivity and a change from isotropic to transversely anisotropic electrical structure, with higher conductivity in the direction of fast propagation for seismic waves. Conductive cooling models predict structure that increases in depth with age, extending to about 30 km at 4.5 Myr ago. We infer, however, that the structure of young oceanic plates is instead controlled by a decrease in water content above a depth of 60 km induced by the melting process beneath the spreading centre.