The results of complex research of cobalt electrodeposition under controllable hydrodynamic conditions with a rotating cylindrical electrode (RCE) from a citrate electrolyte used for obtaining cobalt–tungsten coatings are presented. The influence of the electrolyte pH on the change of the state of the cobalt in the solution, the electrodeposition rate, and the surface morphology is shown. The oscillatory process at potentials close to stationary has been detected and its mechanism is offered. The hydrodynamic conditions (the electric deposition current density increase with the growth of the RCE rotation speed) have been observed have an affect only at Re ≥ 200 and to occur at reaching a certain thicknesses of the electrodeposited layer. The existence of a linear dependence between the current density and the potential of the electric deposition suggests the probability of the formation of a film in the initial period of the deposition.