The eruption of the Cumbre Vieja volcano on 19 September 2021, resulted in the deposition of large quantities of volcanic ash (VA), causing a great impact on the citizens. This work aims to study the properties of this volcanic ash as pozzolanic raw materials to establish their potential use in the development of sustainable cement. Results of chemical and technical characterization are presented. To achieve this goal, Ordinary Portland Cement (OPC) was replaced with standardized percentages of OPC/VA: 10, 25, and 40%. Characterization studies were carried out using chemical analysis of X-ray fluorescence (XRF), chemical quality analysis (QCA), pozzolanicity test (PT) at 8 and 15 days, as well as determining the mechanical strength (MS) at 7, 28, and 90 days. The results obtained by XRF and QCA established that the chemical composition of the VA corresponds to that of the natural pozzolan typical of pyroclastic genesis. The PT test showed that the analyzed samples have a marked pozzolanic nature, both at 8 and 15 days, showing a significant increase in their hydraulic reactivity. Likewise, the MS tests confirmed a continuous increase in mechanical compressive strength, which increased significantly from 7 to 90 days of curing, reaching more than 58 MPa. On the other hand, mechanical tests showed that the three types of dosages used OPC/VA: 10, 25, and 40% were equally effective, with OPC/VA formulations: 10–25% being the most effective. The results obtained in this research could be used by local industries as a guide for the correct use of the volcanic materials of this island, both for the manufacture of construction materials, such as aggregates, and to produce pozzolanic cement with low CO₂ emissions, thus having a positive impact on the environment. Finally, the great natural availability of natural VAs in the surrounding areas of La Palma could cover part of the needs for materials used in the construction and restoration of houses and infrastructures damaged during the volcanic eruption.