Sediment fingerprinting methods aim to determine the relative contribution of different source areas in detrital sediments based on natural properties – fingerprints – of the source areas. Here, we use U/Th–Pb age signatures as fingerprints, assuming that the age signal is not altered during erosion–transportation–deposition events, and given that recent technological advances enable precise dating of large amounts of grains. We introduce a formal inversion method that allows to disentangle the amalgamation of source contributions in detrital zircon data and enables to convert this information into an erosion rate map starting from the spatial distribution of zircon age signatures. Relying on the least‐squares method and using prior and covariance information to deal with non‐uniqueness, we show, using synthetic and natural examples, that we are able to retrieve erosion rate patterns of a catchment when the age distribution and zircon fertility for each source area are well known. Moreover, we show that not only zircon age fingerprints but also other tracers such as mineral content can be used. Furthermore, we found that adding data from samples taken at the outlet of tributaries improves the estimation of erosion rate patterns. We conclude that the least squares inverse model applied to detrital data has great potential for investigating erosion rates.