We study the properties of D and D-* mesons in nuclear matter within a simultaneous self-consistent coupled-channel unitary approach that implements heavy-quark symmetry. The in-medium solution accounts for Pauli blocking effects and for the D and D-* self-energies in a self-consistent manner. We pay special attention to renormalization of the intermediate propagators in the medium beyond the usual cutoff scheme. We analyze the behavior in the nuclear medium of the rich spectrum of dynamically generated baryonic resonances in the C=1 and S=0 sector and their influence on the self-energy and, hence, the spectral function of D and D-* mesons. The D meson quasiparticle peak mixes with Sigma(c)(2823)N-1 and Sigma(c)(2868)N-1 states, whereas the Lambda(c)(2595)N-1 mode is present in the low-energy tail of the spectral function. The D-* spectral function incorporates J=3/2 resonances, and Sigma(c)(2902)N-1 and Lambda(c)(2941)N-1 fully determine the behavior of D-* meson spectral function at the quasiparticle peak. As the density increases, these resonant-hole modes tend to smear out and the spectral functions become broad. We also obtain the D and D-* scattering lengths and the optical potentials for different density regimes. The D meson potential stays attractive, whereas the D-* meson one is repulsive with increasing densities up to twice that of the normal nuclear matter. Compared to previous in-medium SU(4) models, we obtain similar values for the real part of the D meson potential but much smaller imaginary parts. This result could have important implications for the observation of D-0-nucleus bound states.