In this work, the effect of process conditions on the structure, microhardness, and tensile strength of copper—titanium—multiwall carbon nanotubes’ nanocomposite material (NCM) is studied. The goals of the present study are the obtaining a new copper-based nanocomposite material, analysing the mechanisms of its structure formation and investigating the relationship between its structure and the physical and mechanical properties. The criteria for treatment of NCM precursors, which provide for uniform distribution of its components over a specimen bulk, dispersion of multiwall carbon nanotubes’ agglomerates, and optimization of the physical and mechanical properties of the fabricated compositions, are established. Source powders of the materials are mixed in a three-bowl planetary ball mill with acceleration of 50g and pressure on substance particles of about 5 GPa. Such a treatment leads to their mechanical activation and mutual alloying. As shown, after adding both 0.5—1 wt.% of VT 1.0 titanium powder and 0.5—3 vol.% of carbon nanotubes into PMS-1 copper, physical-mechanical properties of NCM specimens fabricated from the component powders after treatment in a planetary-type mill are improved at least twice compared to copper.