A distinct electrodeposition of copper on the external surface of carbon nanotubes (CNT) tissues is demonstrated in two copper electrolytic baths: acid copper sulfate (pH 0.5) and alkaline copper pyrophosphate (pH 8.6). Copper nucleation and growth on the CNT tissue was investigated while applying cathodic polarizations and current transients in a single-step and cost-effective processes. The established copper films are characterized with high uniformity, planarity and excellent adhesion to the densified and bundled CNT tissue substrates, while the surface morphology varies with the chemical composition of the electrolytic bath. Finally, the capability of the copper-coated CNT tissues to function as anode current collectors in a Li-ion battery is shown.