The Groningen gas reservoir, situated in the north‐east of the Netherlands is western Europe's largested gas reservoir. Due to gas production measureable subsidence and seismicity has been detected across this region, attributed to the deformations induced by reservoir pore pressure depletion. We investigate the surface displacement history using a Principal Component Analysis‐based Inversion Method (PCAIM) to combine a diverse set of Optical Leveling, InSAR and GPS data to better constrain reservoir compaction and subsidence history. The generated compaction model is then used in combination with prior pressure depletion models to determine a reservoir uniaxial compressibility. The best fitting model of uniaxial compressibility is time‐independent but spatially variable. The absence of evidence for any significant time‐delay between changes in depletion and compaction rates supports an instantaneous poroelastic reservoir response. The absence of non‐linear yielding at the largest compaction strains suggests anelastic deformations are a minor part of reservoir compaction