The title copper complex, [Cu(H₂P₂O₇)(C₁₅H₁₁N₃)]₂·4.5H₂O, consists of two very similar independent Cu(Tpy)H₂P₂O₇ monomeric units (Tpy is 2,2′:6′,2″-terpyridine) plus four and a half water molecules of hydration, some of which are disordered. Tpy units bind through the usual triple bite via their N atoms, and the H₂P₂O₇^2- anions coordinate through two O atoms from two different phosphate units. Each independent CuN₃O₂ chromophore can be described as a slightly deformed square pyramid, with one of them having a sixth, semicoordinated, O atom from a centrosymmetrically related CuN₃O₂ unit in a weakly bound second apical position suggesting an octahedral environment for the cation and weak dimerization of the molecule. The two independent complex molecules are connected via two strong O–H⋯O interactions between the phosphate groups to form hydrogen-bonded dinuclear units, further linked into [111] columns, resulting in a very complex three-dimensional supramolecular structure through a variety of classical and nonclassical hydrogen bonds, as well as π–π interactions.