The influence of cold rotary forging on the mechanical properties of the Cu/Al–10% La composite, depending on the billet’s reduction ratio, has been studied. The billet was forged from an original diameter of 20 mm to a final diameter of 2.5 mm (e = 4.16). It is shown that the formation of a predominantly subgrain structure with a high density of dislocations in a copper shell, and a predominantly ultrafine grain/subgrain structure in an aluminum rod provides an approximately two-fold increase in the strength of the composite material compared to its components. To clarify the mechanisms of deformation and fracture of the composite samples under tension, the acoustic emission technique was used. It is shown that by choosing the temperature of post-deformation annealing, it is possible to achieve the required balance between strength and plasticity of the composite samples. The electrical conductivity and coefficient of linear thermal expansion of the composite samples have been measured.