In this paper we propose new method to estimate parameters of a damped sinusoidal signal: a frequency, a damping factor, a bias, an amplitude, and a phase. The scheme consists of two cascaded parts. On the first step, the frequency, the damping factor and the bias are estimated. On the second step, these estimates are used to reconstruct the amplitude and the phase. The exponentially damped signals do not provide necessary excitation to parameters identification. To overcome this problem the Dynamic Regressor Extension and Mixing (DREM) method is used to replace third order regression with three first order regression models, where simple relaxation is applied to provide exponential convergence of the estimation error to zero. On the last step, the parameters estimates are calculated from the estimated regression model parameters. Numerical simulations are presented confirming the effectiveness of the proposed methodology.