The synthesis of bimetallic nanoparticles need to be controlled in order to obtain particles of a desired size, spatial structure, and chemical composition. In the synthesis of the Cu–Au nanoparticles studied here, nanoparticles can be obtained through either chemical or physical methods, each of which has its own drawbacks. Although it is very difficult to achieve the required target chemical composition of nanoparticles during chemical synthesis, their size can be stabilized quite well. In turn, physical synthesis methods mainly allow to maintain the required chemical composition; however, the size of the resulting particles varies significantly. To solve this issue, we studied the formation of Cu–Au nanoparticles with different chemical compositions from a gaseous medium using computer molecular dynamics (MD) simulation. The aim was to determine the effect of the concentration of gold atoms on the size and on the actual chemical composition of the formed bimetallic nanoparticles. The modeled region had a cubic shape with a face length of 1350 Bohr radii and contained a total of 91125 copper and gold atoms uniformly distributed in space. Thus, based on the results of the MD simulation, it was concluded that an increase in the percentage of gold atoms in the initial vapor phase led to a decrease in the size of the synthesized nanoparticles. In addition, it was found that clusters with a size of more than 400–500 atoms, regardless of the chemical composition of the initial vapor phase, basically corresponded to a given target composition.