New anthracene based Schiff base ligands L1 and H(L2), their Cu(II) complexes [Cu(L1)Cl2] (1) and [Cu(L2)Cl] (2), (where L1 = N1,N2‐bis(anthracene‐9‐methylene)benzene‐1,2‐diamine, L2 = (2Z,4E)‐4‐(2‐(anthracen‐9‐ylmethyleneamino)phenylimino)pent‐2‐en‐2‐ol) have been prepared and characterized by elemental analysis, NMR, FAB‐mass, EPR, FT‐IR, UV–Vis and cyclic voltammetry. The electronic structures and geometrical parameters of complexes 1 and 2 were analyzed by the theoretical B3LYP/DFT method. The interaction of these complexes 1 and 2 with CT‐DNA has been explored by using absorption, cyclic voltammetric and CD spectral studies. From the electronic absorption spectral studies, it was found that the DNA binding constants of complexes 1 and 2 are 8.7 × 103 and 7.0 × 104 M−1, respectively. From electrochemical studies, the ratio of DNA binding constants K+/K2+ for 2 has been estimated to be >1. The high binding constant values, K+/K2+ ratios more than unity and positive shift of voltammetric E1/2 value on titration with DNA for complex 2 suggest that they bind more avidly with DNA than complex 1. The inability to affect the conformational changes of DNA in the CD spectrum is the definite evidences of electrostatic binding by the complex 1. It can be assumed that it is the bulky anthracene unit which sterically inhibits these complexes 1 and 2 from intercalation and thereby remains in the groove or electrostatic. The complex 2 hardly cleaves supercoiled pUC18 plasmid DNA in the presence of hydrogen peroxide. The results suggest that complex 2 bind to DNA through minor groove binding.