A novel heterogeneous nanocatalyst was fabricated by depositing copper iodide and Fe3O4 nanoparticles on imidazolium‐based ionic liquid‐grafted cellulose and successfully characterized using Fourier transform infrared spectroscopy, thermogravimetric analysis, powder X‐ray diffraction, scanning electron microscopy, energy‐dispersive X‐ray spectroscopy, vibrating sample magnetometry and flame atomic absorption spectrometry. It was employed to catalyse the reaction of terminal acetylenes with sulfonyl azides to afford highly reactive sulfonyl ketenimine intermediates which were subsequently trapped by secondary amines to give N‐sulfonylamidines and N‐sulfonylacrylamidines under solvent‐free conditions at room temperature. Good to excellent yields, very short reaction times, eco‐friendly processing, easy separation and reusability without significant loss of catalytic activity were found to be the notable features of this synthetic protocol.