More than 25% of heat-loss from the Earth's interior occurs via hydrothermal cooling of newly-formed oceanic lithosphere at mid-ocean ridges. In the process, elements (including economically-relevant base and precious metals) are re-distributed and concentrated in seafloor massive sulphide (SMS) deposits. A recent estimate1 suggested that the amount of metal being deposited at the presently-active ridges is not economically significant (with a total copper+zinc inventory equal to only one year of global copper+zinc consumption), but also highlighted the unknown potential of older seafloor, for which no viable exploration models existed. Here we present the results of hydrothermal exploration along 3000 km of the Mid-Atlantic Ridge (representing almost 5% of the total length (64.000km) of the global mid-ocean ridge system and over 8% of the economically more interesting slow-spreading (<40mm/yr) ridges). We find significant correlations between axial morphology as determined by ship-mounted multibeam and the presence of high-temperature hydrothermal venting determined from water column studies. Using these relationships we can, for the first time, predict the location of extinct hydrothermal deposits within the plate interior solely based on ship-based multibeam surveys