We report two easily synthesizable, reusable and morphology-controlled copper nanostructures grafted over rGO (i.e., rGO-CuNRs and rGO-CuNPs). The structure, morphology and the composition of the nanocatalysts have been characterized by TEM, SEM, XPS, PXRD and TGA analyses. These nanocatalysts having ‘rod-like’ (for rGO-CuNRs) as well as spherical (for rGO-CuNPs) nanostructures promoted one-pot multicomponent click reaction between in situ generated organic azide and phenyl acetylene to afford a 1,2,3-triazole derivative (L). The nanocomposites containing ‘rod-like’ morphology exhibited remarkably higher catalytic activity as compared to spherical nanoparticle counterparts. Interestingly, rGO-CuNRs exhibited rapid synthesis (∼ 60 min) of L with excellent yield (∼ 92%) involving pure water as a clean and eco-friendly reaction medium. A low copper loading, high recyclability upto 7 times with the negligible loss of catalytic activity and easy workup process is presented. The click product (L) will find promising applications as ‘polydentate click chelator’ to generate metallo-supramolecular assemblies in biomimetic chemistry.