Olive oil and pig productions are important industries in Portugal that generate large volumes of wastewater with high organic load and toxicity, raising environmental concerns. The principal objective of this study is to energetically valorize these organic effluents—piggery effluent and olive mill wastewater—through the anaerobic digestion to the biogas/methane production, by means of the effluent complementarity concept. Several mixtures of piggery effluent were tested, with an increasing percentage of olive mill wastewater. The best performance was obtained for samples of piggery effluent alone and in admixture with 30% of OMW, which provided the same volume of biogas (0.8 L, 70% CH4), 63/75% COD removal, and 434/489 L CH4/kg SVin, respectively. The validation of the process was assessed by molecular evaluation through Next Generation Sequencing (NGS) of the 16S rRNA gene. The structure of the microbial communities for both samples, throughout the anaerobic process, was characterized by the predominance of bacterial populations belonging to the phylum Firmicutes, mainly Clostridiales, with Bacteroidetes being the subdominant populations. Archaea populations belonging to the genus Methanosarcina became predominant throughout anaerobic digestion, confirming the formation of methane mainly from acetate, in line with the greatest removal of volatile fatty acids (VFAs) in these samples.