Copper-CNT (carbon nanotube) composite materials are promising alternatives to conventional conductors in applications ranging from interconnects in microelectronics to electrical cabling in aircraft and vehicles. Unfortunately, exploiting the full potential of these composites is difficult due to the poor Cu-CNT electro-mechanical interface. We demonstrate through large-scale ab initio calculations and sonication experiments that this problem can be addressed by CNT surface modification. Our calculations show that covalent functionalization of CNTs below 6.7 at% significantly improves Cu-CNT wetting and the mechanical properties of the composite. Oxidative pre-treatment of CNTs enhances the Young's modulus of the composite by nearly a factor 3 above that of pure Cu, whereas amination slightly improves the electrical current density with respect to the unmodified Cu-CNT system in the high bias regime. However, only nitrogen doping can effectively improve both the mechanical and electrical properties of the composite. As the experiments show, consistent with the calculations, substitutional doping with nitrogen effectively improves adhesion of the CNT to the Cu matrix. We also predict an improvement in the mechanical properties for the composite containing doped double-wall CNTs. Moreover, the calculations indicate that the presence of nitrogen dopants almost doubles locally the transmission through the nanotube and reduces the back scattering in the Cu matrix around the CNT. The computed electrical conductance of N-doped Cu-CNT "carpets" exceeds that of an undoped system by ∼160%.