Dielectric relaxation of aqueous protein solutions show many anomalous properties. For example, (i) protein solutions have higher static dielectric constant compared to that of pure water, (ii) the real part of the dielectric function (DF) exhibits a crossover with varying concentration, and (iii) the imaginary part of DF exhibits a bimodal frequency dependence. There is no coherent microscopic explanation available for any of these phenomena. Here we present the first unified, microscopic theory of the dielectric relaxation spectra of an aqueous protein solution that explains all the above anomalies, with excellent agreement with all the known experimental results.