We present an approach for calculating the electronic structure and transport properties of nanoscopic conductors that takes into account the dynamical correlations for strongly interacting d or f electrons by combining density-functional theory calculations with the dynamical mean-field theory. While the density-functional calculation yields a static mean-field description of the weakly interacting electrons, the dynamical mean-field theory explicitly takes into account the dynamical correlations of the strongly interacting d or f electrons of transition metal atoms. As an example we calculate the electronic structure and conductance of Ni nanocontacts between Cu electrodes. We find that the dynamical correlations of the Ni 3d electrons give rise to quasiparticle resonances at the Fermi level in the spectral density. The quasiparticle resonances, in return, lead to Fano line shapes in the conductance characteristics of the nanocontacts similar to those measured in recent experiments of magnetic nanocontacts.