This paper presents a new diagnostic tool for the inference of the thermal, dynamic, and magnetic properties of the solar chromosphere. It consists of a non-LTE inversion code of Stokes profiles induced by the Zeeman effect in magnetized stellar atmospheres. This code is the generalization, to the non-LTE Stokes transfer case, of the inversion code for unpolarized line profiles of Socas-Navarro, Ruiz Cobo, & Trujillo Bueno. It is based upon a full non-LTE multilevel treatment of Zeeman line transfer in which the thermal, magnetic, and dynamic properties of the atmospheric model are adjusted automatically by means of nonlinear least-squares-fitting techniques until a best fit to the observed Stokes profiles is obtained. Our non-LTE inversion approach is based on the concept of response functions, which measure the emergent Stokes profiles' first-order reaction to changes in the atmospheric parameters. We generalize our fixed departure coefficients (FDC) approximation in order to allow fast computation of such response functions in the present non-LTE Zeeman line transfer context. We present several numerical tests showing the reliability of our inversion method for retrieving the information about the thermodynamics and the magnetic field vector that is contained in the polarization state of the chosen spectral lines. We also explore the limitations of the inversion code by applying it to simulated observations where the physical hypotheses on which it is based on are not met. Finally, we apply our non-LTE Stokes inversion code to real spectropolarimetric observations of a sunspot observed in the IR triplet lines of Ca II. As a result, a new mean model of the sunspot chromosphere is provided.