A microscopic theory is presented for the local moment formation near a non-magnetic impurity or a copper defect in high-Tc superconductors. We use a renormalized meanfield theory of the t − J model for a doped Mott insulator and study the fully self-consistent, spatially unrestricted solutions of the d-wave superconducting (SC) state in both the spin S = 0 and S = 1/2 sectors. We find a transition from the singlet d-wave SC state to a spin doublet SC state when the renormalized exchange coupling exceeds a doping dependent critical value. The induced S = 1/2 moment is staggered and localized around the impurity. It arises from the binding of an S = 1/2 nodal quasiparticle excitation to the impurity. The local density of states spectrum is calculated and connections to NMR and STM experiments are discussed.PACS numbers: 74.25.Jb,74.25.Ha,75.20.Hr,74.20Mn The local electronic structure near non-magnetic impurities in high-T c superconductors has attracted wide attention recently. A series of NMR experiments in YBa 2 Cu 3 O 7−x (YBCO) have shown that with the substitution of nonmagnetic Zn/Li for the Cu atoms in the CuO 2 plane, an S = 1/2 staggered magnetic moment is generated on the Cu ions in the vicinity of the impurity sites [1,2,3,4,5,6,7,8]. Below the superconducting transition temperature, the moment is partially screened in optimally doped YBCO, but remains unscreened down to the lowest temperatures in the underdoped regime [3,2]. Low-temperature STM experiments [9] have directly observed the local electronic structure around the Zn impurity atoms on the surface of superconducting Bi 2 Sr 2 CaCu 2 O 8+x (BSCCO). The tunneling differential conductance above the Zn site exhibits a sharp in-gap resonance peak near zero bias (-1.5meV) for electrons tunneling out of the sample [9].While the presence of a resonance impurity state is consistent with the strong local potential scattering near the impurity [10,11], the latter does not account for the local magnetic moment induced by nonmagnetic impurities observed by NMR. This has led to attempts to identify the low energy conductance peak with the Kondo resonance resulting from the Kondo screening of the local moment by the superconducting (SC) electrons [12]. However, the formation of the local moment itself near nonmagnetic impurities in a d-wave superconductor has not been addressed. In this paper, we present a theory which simultaneously explains the local moment formation and predicts a strong low energy resonance in the local density of states (LDOS) spectrum.We study the local moment formation in d-wave superconductors in proximity to Mott insulators. In the resonance-valence-bond (RVB) picture [13], the electrons are paired into spin singlets, which are mobilized by the doped holes and condense into the SC state below T c . A nonmagnetic impurity atom such as Zn/Li or a Cu vacancy locally breaks a singlet, creating an unpaired spin. This extra S = 1/2 moment can be self-consistently trapped by the local impurity potential, forming a local moment confine...