Abstract This paper presents the explicit formulas for optimal tuning of the tuned mass damper (TMD) for damping edgewise vibrations in rotating wind turbine blades. A 2-DOF model is first established for the rotating blade-TMD system, which acts as the basis for analytically deriving the optimal frequency-tuning and the optimal damping-tuning formulas. Two optimality criteria are considered, one based on equal dynamic amplification at two neutral frequencies and the other one based on equal modal damping ratio of the free vibration modes. As a result, two slightly different optimal frequency-tuning formulas are obtained. The formula for optimal TMD damping ratio is obtained by means of dynamic amplification analysis, and the optimal damping ratio turns out to be dependent on the rotor rotational speed. Comparison of the two optimal frequency-tuning formulas are performed in terms of the dynamic amplification curves and the root loci, using the NREL 5 MW wind turbine as the numerical example. For realistic rotor rotational speeds, the two optimal frequency-tuning formulas lead to almost identical TMD parameters.