In this work, the properties of concrete modified with dosages of natural pozzolans (NP) in substitution of cement or superfine aggregates were evaluated. Proportions of 20/80 pozzolan/cement or pozzolan/superfine aggregates were selected for the additions of quarry and tuff pozzolans. Pozzolanic activity, durability, compressive strength, characteristic resistance, settling consistency, density, electrical resistivity, depth of water penetration, accessible porosity, and carbonation and chloride penetration were determined for the resulting concrete mixtures, and they were subsequently compared to the values obtained for the reference concrete batches without additions. The results of the cementitious mixtures supplemented with tuff (PZT) and quarry (PZQ) pozzolans, expressed in mmol/L, are consistent with the pozzolanism test, with [Ca(OH)2]/[OH−] ratios at 7 days are 6.03/60.19 for PZQ and 1.78/92.78 PZT. In addition to the pozzolanic activity at these dosages, the characteristic resistance and durability parameters required by EHE-08 were verified. Particular attention was given to the determination of the diffusion of chloride ions, introducing an instrumental modification of the accelerated integral method. The modification provides values of diffusion coefficients similar to those obtained by the other methods with the advantage of greater stability and quality of the measurement.