Most of the near-field source localization methods are developed with the approximated signal model, because the phases of the received near-field signal are highly non-linear. Nevertheless, the approximated signal model based methods suffer from model mismatch and performance degradation while the exact signal model based estimation methods usually involve parameter searching or multiple decomposition procedures. In this paper, a search-free near-field source localization method is proposed with the exact signal model. Firstly, the approximative estimates of the direction of arrival (DOA) and range are obtained by using the approximated signal model based method through parameter separation and polynomial rooting operations. Then, the approximative estimates are corrected with the exact signal model according to the exact expressions of phase difference in near-field observations. The proposed method avoids spectral searching and parameter pairing and has enhanced estimation performance. Numerical simulations are provided to demonstrate the effectiveness of the proposed method.