A series of new cationic and neutral (Ar‐BIAN)copper(I) complexes [in which Ar‐BIAN = bis(aryl)acenaphthenequinonediimine] was synthesised and characterised by elemental analysis, 1D and 2D NMR spectroscopy and single‐crystal X‐ray diffraction. The cationic complexes of the general formula [Cu(Ar‐BIAN)L2]BF4 [L2 = (PPh3)2 (1), dppe (2), dppf (3), (AsPh3)2 (4); Ar = 4‐iPrC6H4 (a), 4‐MeOC6H4 (b), 4‐NO2C6H4 (c), 2‐iPrC6H4 (d), Ph2PCH2CH2PPh2 (dppe), (Ph2PC5H4)2Fe (dppf)] were synthesised by reaction of [Cu(EPh3)4]BF4 (E = P or As) and equimolar amounts of Ar‐BIAN ligands, or by reaction of equimolar amounts of [Cu(NCMe)4]BF4, 4‐iPrC6H4‐BIAN (a) and diphosphanes dppe or dppf, in dichloromethane, whereas the neutral complexes of the types [CuX(Ar‐BIAN)(EPh3)] [X = Cl, E = P (5); X = I, E = P (6); X = Cl, E = As (9)] and [{CuX(Ar‐BIAN)}2] [X = Cl (7), I (8); Ar = a, b, c, d, 2,4,6‐Me3C6H2 (e), 2,6‐iPr2C6H3 (f)] were prepared by reaction of CuCl or CuI with equimolar amounts of Ar‐BIAN and EPh3 (E = P, As or Sb) in acetonitrile under reflux conditions. The type of ancillary ligand EPh3 and the aryl substituents on Ar‐BIAN play crucial roles in determining the formation of cationic or neutral copper(I) complexes. No copper(I) complexes containing coordinated SbPh3 were isolated; all the corresponding attempts led to dimeric complexes 7 or 8. Most of the complexes crystallised easily. Their study by X‐ray diffraction revealed distorted‐tetrahedral geometries around the copper(I) centres, which are quite influenced by the various aryl substituents on Ar‐BIAN and the ancillary ligands EPh3. All complexes 1–9 except cationic dppf derivative 3a are active catalysts for cycloaddition reactions of alkynes and azides, and also show good tolerance towards functionalised substituents of alkynes and azides. Among them, the PPh3‐coordinated complexes 1, 5 and 6 afforded the highest catalytic activities [turnover frequency = 26.9–45.7 h–1].