Three neutral Cu(I) complexes bearing 2,6‐dimethylphenyl isocyanide (CNXyl) and different triatomic pseudohalogens (SCN−, OCN− and N3−) as ligands were efficiently synthesized and characterized. The solid‐state structures were unambiguously determined through single‐crystal X‐ray diffraction, revealing unexpected bridging coordination modes in the case of OCN− and N3−. All the complexes were tested for azide‐alkyne cycloaddition (CuAAC), showing interesting catalytic activity towards the formation of 1,4‐disubstituted‐1,2,3‐triazoles for the cyanato and the azido Cu(I) complexes. Both species afforded yields above 90% with 0.5 mol% of catalyst at 50°C for 24 h. Several alkynes and azides were tested using the more active azido Cu(I) complex, affording the corresponding triazoles in high yields. The azido Cu(I) complex also induced the intramolecular CuAAC in the presence of dimethyl acetylenedicarboxylate and benzyl bromide/phenylacetylene.