In this research, copper nanocomposites reinforced by graphene nanoplatelets (GNPs) were fabricated using a wet mixing method followed by a classical powder metallurgy route. In order to find the best dispersion technique, ball milling and wet mixing were chosen. Qualitative evaluation of the structure of the graphene after mixing indicated that the wet mixing is an appropriate technique to disperse the GNPs. Thereafter, the influence of graphene content on microstructure, density, hardness, elastic modulus, and thermal expansion coefficient of composites was investigated. It was shown that by increasing the graphene content the aggregation of graphene is more obvious and, thus, these agglomerates affect the final properties adversely. In comparison with the unreinforced Cu, Cu–GNP composites were lighter, and their hardness and Young’s modulus were higher as a consequence of graphene addition. According to the microstructural observation of pure copper and its composites after sintering, it was concluded that grain refinement is the main mechanism of strengthening in this research. Apart from the mechanical characteristics, the coefficient of thermal expansion of composites decreased remarkably and the combination of this feature with appropriate mechanical properties can make them a promising candidate for use in electronic packaging applications.