The nickel isotopes are described in terms of strongly admixed spherical shell-model configurations of neutrons occupying the 2p32, 1f52, and 2p12 orbits. A set of effective-interaction matrix elements is deduced which accurately reproduces the spectra of the Ni isotopes from Ni58 to Ni67. The wave functions resulting from the calculation of the energy levels are then used to calculate the single-nucleon spectroscopic factors. These are in fairly good agreement with the experimental spectroscopic factors found in pickup and stripping experiments. In addition, some of the results from two-nucleon transfer reactions are compared with the predictions of the present model. Using the wave functions obtained and an effective charge for the neutron, the E2 transition probabilities in the even-mass isotopes of Ni are calculated and found to be in agreement with experimental facts.