We investigate the 19 September 2021 eruption of the Cumbre Vieja volcano (La Palma, Canary Islands, Spain). In particular, we analyze the Differential Interferometric Synthetic Aperture Radar (DInSAR) measurements obtained by processing Sentinel‐1 images acquired from both ascending and descending orbits. First, we show the importance, for oceanic islands like La Palma, of investigating DInSAR products retrieved from time series, instead of single interferograms, to effectively remove possible atmospheric artifacts within the displacement measurements. Subsequently, we invert the retrieved data through analytical modeling. Our results highlight that a sill–like source was active in the pre–eruptive phase (8–16 September), whereas the action of two dikes prevailed during the co‐eruptive phase (17–22 September). This evolution suggests a process of magma rising through a network of interconnected sills and dikes. The seismicity, that preceded and accompanied the onset of the eruption, is consistent with our findings. Plain Language Summary Since 19 September 2021, an intense eruptive activity has begun at Cumbre Vieja volcano (La Palma, Canary archipelago, Spain), causing huge social and economic damage. The eruption was preceded and accompanied by numerous phenomena, such as gas emissions and seismic activity. In this work, we exploit the Differential Interferometric Synthetic Aperture Radar (DInSAR) measurements, obtained by processing Sentinel‐1 images, to quantify the retrieved pre‐ and co‐eruptive deformation patterns. In particular, this eruption provided us the opportunity to show the importance, for oceanic islands like La Palma, of investigating DInSAR products retrieved from time series, instead of conventional single interferograms, to effectively remove possible atmospheric artifacts within the displacement measurements. Subsequently, we invert the retrieved surface deformation measurements to investigate the geometries of the volcanic sources responsible for the observed deformations. Our results show the evolution of this eruptive phenomenon from the pre‐to the co‐eruptive phases, suggesting that a complex network of sills and dikes has allowed the magma rising. Moreover, our findings are in good agreement with the recorded seismicity and several geophysical evidence. Key Points We retrieve the pre‐ and co‐eruptive deformation patterns of Cumbre Vieja volcano through an advanced processing of Sentinel‐1 radar data We show that a sill‐like source was active in the pre‐eruptive phase, whereas the action of two dikes prevailed in the co‐eruptive one The retrieved sources are consistent with magma rising through a network of interconnected sills and dikes, and the seismicity evolution