The present paper focused on the removal of Tartrazine and indigo carmine from aqueous solutions by cobalt hydroxide nanosorbent. This novel and efficient nanosorbent were successfully used to remove two anionic dyes from aqueous solutions in single and binary systems. The characterization of sorbent was carried out with scanning electron microscopy micrographs, X‐ray diffraction, and Fourier transform infrared spectroscopy analysis. The simplex‐lattice mixture design was employed for optimization of adsorption process. The effective factors on adsorption such as pH, m (amount of sorbent), and C (initial concentrations of dyes) were considered using crossed mixture‐process design. The proposed quadratic model resulted from the mixture design approach fitted very well to the experimental data. Isotherm modeling and kinetic investigations showed that sips, modified sips, and pseudo‐second‐order models describe both the adsorption equilibrium and kinetic behavior well, respectively.