The momentum-resolved electronic structure of ultrathin films of Ni on Cu(001) is investigated by angle-resolved photoemission in the thickness range between 2 and 6 monolayers and by first-principles slab calculations. While the sp-band Fermi surface of Ni shows a full three-dimensional bulklike topology down to the thinnest films, the d-band Fermi surface rearranges from a bulklike configuration in the thick films to a two-dimensional topology in the thinnest films. The reduced number of d holes in the thin films is explained with the rearrangement of the characteristic K-point lobe of the Ni Fermi surface.