Tectonic activity generates topography, and the variability of tectonic forcing is responsible for topographic patterns and variability of relief in fluvial landscapes. Despite this basic relation, the inverse problem, by which features of the topography are used for inferring tectonic uplift rates, has proven challenging. Here we develop formal linear inversion schemes to infer a record of the rate of relative uplift as a function of space and time from the long profiles of rivers. The relative uplift rate is the difference between the rates of rock uplift and of the base level change. The inversion schemes are based on a closed-form analytic solution to the transient linear stream power model, and to increase model resolution they make use of the multiplicity of information made available by multiple rivers and their tributaries. The distribution of the fluvial response time to tectonic perturbations is a key component of the inversion scheme, as this determines which tectonic events are preserved in the topography. We develop two inversion parameterizations that differ in their assumptions about the tectonic forcing: space-invariant and time-space variability with an assumed spatial distribution. The inversion schemes are applied to the Inyo Mountains, an uplifted block along the western boundary of the Basin and Range Province in California. Inversion results indicate that the range has been experiencing an acceleration of the relative uplift in the past ∼2-3 Ma. We use the inversion results to constrain the paleotopography and paleo-erosion rate along the range and to recover the throw rate history along the fault that bounds the Inyo range.