Given its sensitivity to anatomical variations, particle therapy is expected to benefit strongly from reliable on-line treatment verification. Making use of a large fraction of the secondary particles available, hybrid prompt gamma-ray and fast neutron imaging is a promising approach for this purpose. We present a simulation study introducing a novel method for range reconstruction by means of these particles. To this end, the passage of a proton beam through a patient and the detection of secondary particles in a dedicated detector array were simulated by Monte Carlo particle transport calculations. Anatomical variations were mimicked by adding or removing tissue to the patient. The secondary particle production vertices were reconstructed from the events registered by the detector based on scatter kinematics and maximum likelihood expectation maximisation. The vertices were projected onto the beam axis and the most predictive features of the resulting distributions were identified from a standardised feature set by forward feature selection and the Least Absolute Shrinkage and Selection Operator (LASSO). A range-shift sensitivity of 1 mm or less was reached at intensities of 1.2×10⁷ protons per spot with fast neutrons, and at 2.6×10⁷ protons per spot with prompt gamma-rays. These results demonstrate the potential of particle treatment verification by fast neutrons and prompt gamma-rays and strengthen the potential of this hybrid system for clinical application.