A new series of heteroleptic copper(II) complexes of the type Cu(L1−3)(diimine) (1–6) have been synthesized using three pyridazine-based ligands (3-chloro-6-(salicylidenehydrazinyl)pyridazine (HL1), 3-chloro-6-(4-diethylaminosalicylidenehydrazinyl)pyridazine (HL2) and 3-chloro-6-(5-bromosalicylidenehydrazinyl)pyridazine (HL3), and diimine (2,2′-bipyridine (bpy) or 1,10-phenanthroline (phen)) as co-ligands. The ligands and their copper(II) complexes have been characterized by elemental analyses and spectroscopic methods. The copper(II) complexes display ligand-field band in the region 641–661 nm suggesting square pyramidal geometry. The optimized structures of the complexes and their molecular orbital calculations obtained by the density functional theory (DFT) also showed five coordinated distorted square pyramidal geometry around the copper(II) ion. The cyclic voltammetric analyses of copper(II) complexes exhibit one-electron irreversible reduction wave (Epc = −0.596 to −0.641 V) in the cathodic potential region. Anti-proliferative activity of the complexes against breast cancer MDA-MB-231 cell line was evaluated by MTT cell proliferation assay, and the clonogenic assay revealed improved cytotoxicity for the complexes with potency higher than the standard drug cisplatin. Since the complexes 3 and 4 with diethylamino substituent displayed higher anti-proliferative activity than the other complexes, these complexes were chosen for apoptosis and cell cycle analysis. The apoptosis induction was analyzed by AO/EB staining, and the flow cytometry showed the inhibition of cell growth at the S-phase of the cell cycle. Additionally, the interaction of copper(II) complexes with FGFR kinase receptor have been studied by in silico molecular docking studies.