Four bacterial strains capable of growing in the presence of tannic acid as sole carbon and energy source were isolated from olive mill waste mixtures. 16S rRNA gene sequencing assigned them to the genus Klebsiella. The most efficient strain, Klebsiella sp. strain C2A, was able to degrade 3.5 g L−1 tannic acid within 35 h with synthesizing gallic acid as main product. The capability of Klebsiella sp. strain C2A to produce tannase was evidenced at high concentrations of tannic acid up to 50 g L−1. The bacteria adapted to the toxicity of tannic acids by an increase in the membrane lipid fatty acids degree of saturation, especially in the presence of concentrations higher than 20 g L−1. The highly tolerant and adaptable bacterial strain characterized in this study could be used in bioremediation processes of wastes rich in polyphenols such as those derived from olive mills, winery or tanneries.