Two water‐soluble 6‐(pyrazin‐2‐yl)‐1,3,5‐triazine‐2,4‐diamino (pzta)‐based Cu(II) complexes, namely [Cu(l‐Val)(pzta)(H2O)]ClO4 (1) and [Cu(l‐Thr)(pzta)(H2O)]ClO4 (2) (l‐Val: l‐valinate; l‐Thr: l‐threoninate), were synthesized and characterized using elemental analyses, molar conductance measurements, spectroscopic methods and single‐crystal X‐ray diffraction. The results indicated that the molecular structures of the complexes are five‐coordinated and show a distorted square‐pyramidal geometry, in which the central copper ions are coordinated to N,N atoms of pzta and N,O atoms of amino acids. The interactions of the complexes with DNA were investigated using electronic absorption, competitive fluorescence titration, circular dichroism and viscosity measurements. These studies confirmed that the complexes bind to DNA through a groove binding mode with certain affinities (Kb = 4.71 × 103 and 1.98 × 103 M−1 for 1 and 2, respectively). The human serum albumin (HSA) binding properties of the complexes were also evaluated using fluorescence and synchronous fluorescence spectroscopies, indicating that the complexes could quench the intrinsic fluorescence of HSA in a static quenching process. The relevant thermodynamic parameters revealed the involvement of van der Waals forces and hydrogen bonds in the formation of complex–HSA systems. Finally, molecular docking technology was also used to further verify the interactions of the complexes with DNA/HSA.