Alloy nanoparticles (nanoalloys) are widely applied in heterogeneous catalysts, advanced electrodes, biomaterials, and other areas. The properties of nanoalloys can be tuned to a significant extent by their structures and compositions, which are governed by the employed synthetic procedure. Often such synthesis occurs in non‐equilibrium conditions and yields nanoalloys with structures and properties that are different from those obtained in thermodynamic equilibrium. In this work, we characterize how the non‐equilibrium conditions during the synthesis of Cu–Au alloys via physical vapor deposition (PVD) affect their morphology, composition, electronic structure, and reactivity in CO oxidation. We used molecular dynamics to simulate the PVD synthesis of Cu–Au nanoalloys through the non‐isothermal aggregation of Cu and Au atoms at a 3:1 ratio in the Ar atmosphere to obtain realistic structures of Cu–Au nanoparticles. Due to the different aggregation kinetics of Au and Cu atoms, the average Au concentration in the obtained Cu–Au particles varied between 14% and 50% depending on the nanoparticle size and the aggregation time. Density functional simulations revealed that the reactivity of the obtained Cu–Au clusters toward CO and oxygen as well as Brønsted–Evans–Polanyi relations for CO oxidation significantly depend on whether the clusters had fcc, icosahedral, or amorphous structures and do not strongly correlate with the d‐band centers of the adsorption sites. Our study highlights the importance of the non‐equilibrium character of nanoalloy structure and composition for their electronic structure and catalytic properties. The performed analysis of the reactivity of Cu–Au clusters with realistic structures in CO oxidation will help the optimization of Cu–Au catalysts for this societally important reaction.