The electrodeposition of copper on pyrolytic graphite from CuSO4 or Cu(NO3)2 in a 1.8 M H2SO4 aqueous solution was investigated. The Cu deposits were formed potentiostatically and characterized by electrochemical methods, scanning electron microscopy, energy dispersive X-ray and X-ray photoelectron spectroscopy. It was found that the deposition of copper in the presence of CuSO4 induced the codeposition of sulfate anions. In addition, electrochemical quartz crystal microbalance revealed that the increase of the Cu mass was higher than expected from Faraday’s law with the CuSO4/H2SO4 solution. These results confirmed the specific adsorption of anions during the Cu deposition. On the other hand, the use of Cu(NO3)2 resulted in a non-contaminated surface with different surface morphologies. The Cu nuclei size, the population density and the surface coverage were monitored as a function of the deposition potential. From the analysis of the chronoamperometric curves, the nucleation kinetics was studied by using various theoretical models. Independently of the Cu source, the nucleation mechanism follows a three-dimensional (3D) process. Copper nucleates according to an instantaneous mode when the deposition potential is more negative than −300 mV versus Ag/AgCl, while the nucleation was interpreted in terms of a progressive mode at −150 mV. The nuclei population densities were also determined by using two common fitting models for 3D nucleation and growth (Scharifker–Mostany and Mirkin–Nilov–Heerman–Tarallo). Their values are reported here as a function of the deposition potential.