A series of Ar-BIAN-based copper(I) complexes (where Ar-BIAN = bis(aryl)acenaphthenequinonediimine) were synthesised and characterised by 1H and 13C NMR spectroscopies, FT-IR spectroscopy, MALDI-TOF-MS spectrometry, cyclic voltammetry and single crystal X-ray diffraction. The bis-chelated complexes of general formula [Cu(Ar-BIAN)2]BF4 (where Ar = C6H5 (1), 4-iPrC6H4 (3), 2-iPrC6H4 (4)) were prepared by reaction of [Cu(NCMe)4]BF4 with two equivalents of the corresponding Ar-BIAN ligands, in dichloromethane, while the mono-chelated complexes of the type [Cu(Ar-BIAN)L2]BF4 (where Ar = 2,6-iPr2C6H3, L = PhCN (6); Ar = 4-iPrC6H4, L = PPh3 (7)) were readily accessible by treatment of [Cu(NCR)4]BF4 (R = Me, Ph) with one equivalent of the corresponding Ar-BIAN ligands in the absence or presence of two equivalents of PPh3, in the same solvent. The structures of complexes 3, 4, 6 and 7 were obtained by single crystal X-ray diffraction, showing distorted tetrahedral geometries around the copper centres in all cases. The electrochemical studies of these complexes and of the already reported [Cu(2,4,6-Me3C6H2-BIAN)2]BF4 (2) and [Cu(2,6-iPr2C6H3-BIAN)(NCMe)2] (5), demonstrated that the bis-chelated complexes 1–4 undergo a reversible one-electron reduction or oxidation processes on copper, while the mono-chelated complexes 5–7 show a partially reversible oxidation and an irreversible reduction feature. Both kinds of (Ar-BIAN)copper(I) complexes are active catalysts for the copper(I)-catalysed azide–alkyne cycloaddition reaction (CuAAC). Complex 7, bearing PPh3 ligands, exhibits the highest catalytic activity, which is comparable with that of the typical CuSO4–sodium ascorbate catalyst system.