We study the problem of signal source localization using differential received signal strength (DRSS) measurements. We begin by presenting verifiable geometric conditions for sensor deployment that ensure the model’s asymptotic localizability. Then we establish the consistency and asymptotic efficiency of the maximum likelihood (ML) estimator. However, computing the ML estimator is challenging due to relying on solving a non-convex optimization problem. To address this, we propose an asymptotically efficient two-step estimator that matches the ML estimator’s asymptotic properties while achieving low computational complexity (linear in the number of measurements). The primary challenge lies in obtaining a preliminary consistent estimate in the first step. To achieve this, we construct a linear least-squares (LS) problem through algebraic operations on the nonlinear measurement model to obtain a closed-form solution. This solution is biased due to the correlation between the regressors and the noise of the linear model.We eliminate the bias using the data to yield an asymptotically unbiased and consistent estimate. In the second step, we perform a single Gauss-Newton (GN) iteration using the preliminary consistent estimate as the initial value, achieving the same asymptotic properties as the ML estimator. Finally, simulation results demonstrate the superior performance of the proposed two-step estimator over existing methods for large sample sizes.