Kinetics of copper deposition onto an Au(111) surface from sulfuric acid electrolyte, was evaluated using potentiostatic current transients. Measurements were conducted employing a new and nontraditional method, with gold electrode completely free from copper deposit at the beginning of the potential step (i.e., deposition process). The current transients obtained clearly show partial contribution from copper underpotential deposition (UPD) and copper overpotential deposition (OPD) processes. Quantitative evaluation of experimental transients was performed with the recently developed method for theoretical transient computer simulation. Detailed analysis of the kinetic parameters shows that copper UPD could be characterized as a two-dimensional nucleation and growth limited by the lattice incorporation (2D-LI) process and copper OPD as a three-dimensional nucleation process limited by diffusion-controlled growth (3D-DC). The UPD seems to be an inevitable part of the deposition process and takes place prior to OPD, regardless of the potential applied. Therefore, UPD should be treated as an early stage of the deposition process. Furthermore, our results show that the kinetics differs depending on whether deposition is initiated from a clean, bare Au(111) surface or from a gold surface already coated with a copper UPD adlayer. This indicates the role of the UPD process and the UPD adlayer on the course of OPD. Differences observed in deposition kinetics between electrolytic baths at pH 2 and 4 were likely due to adsorption of different sulfate species (sulfate or bisulfate anions) on the copper-deposit-modified Au(111) substrate (UPD, epitaxial monolayer) or bulk deposit adlayer (OPD).