Copper matrix composites reinforced by copper foams with uniformly embedded carbon nanotubes (CNTs) were prepared by electrodeposition and spark plasma sintering (SPS). The microstructure and mechanical properties of the composite foams and bulk composites were characterized or tested by Raman spectroscopy, scanning electron microscopy (SEM), transmission electron microscopy (TEM), and tensile tester, respectively. The results show that the CNTs are uniformly dispersed and embedded in the copper foams by electrodeposition, which preserve as reinforcing skeletons in the subsequent SPS sintered composites. Significant improvements of the tensile strength up to 341.32 MPa and the elongation value of 35.59% are obtained for the CNTs/Cu foam reinforced copper composites, showing a simultaneous achievement of high strength and high ductility with such a three-dimensional skeleton reinforced composite structure. The strengthening mechanisms are also discussed.