The Crab Nebula is a unique laboratory for studying the acceleration of electrons and positrons through their non-thermal radiation. Observations of very-high-energy γ rays from the Crab Nebula have provided important constraints for modelling its broadband emission. We present the first fully self-consistent analysis of the Crab Nebula’s γ-ray emission between 1 GeV and ∼100 TeV, that is, over five orders of magnitude in energy. Using the open-source software package GAMMAPY, we combined 11.4 yr of data from the Fermi Large Area Telescope and 80 h of High Energy Stereoscopic System (H.E.S.S.) data at the event level and provide a measurement of the spatial extension of the nebula and its energy spectrum. We find evidence for a shrinking of the nebula with increasing γ-ray energy. Furthermore, we fitted several phenomenological models to the measured data, finding that none of them can fully describe the spatial extension and the spectral energy distribution at the same time. Especially the extension measured at TeV energies appears too large when compared to the X-ray emission. Our measurements probe the structure of the magnetic field between the pulsar wind termination shock and the dust torus, and we conclude that the magnetic field strength decreases with increasing distance from the pulsar. We complement our study with a careful assessment of systematic uncertainties.