We describe a software package, TomOpt, developed to optimise the geometrical layout and specifications of detectors designed for tomography by scattering of cosmic-ray muons. The software exploits differentiable programming for the modeling of muon interactions with detectors and scanned volumes, the inference of volume properties, and the optimisation cycle performing the loss minimisation. In doing so, we provide the first demonstration of end-to-end-differentiable and inference-aware optimisation of particle physics instruments. We study the performance of the software on a relevant benchmark scenario and discuss its potential applications. Our code is available on Github.