With a combination of magnetic susceptibility measurements and low-temperature neutron diffraction analyses, the magnetic structure of Li2FeP2O7 cathode has been solved. This pyrophosphate Li2FeP2O7 compound stabilizes into a monoclinic framework (space group P2(1)/c), having a pseudolayered structure with the constituent Li/Fe sites distributed into MO6 and MO5 building units. The magnetic susceptibility follows a Curie-Weiss behavior above 50 K. Li2FeP2O7 shows a long-range antiferromagnetic ordering at T(N) = 9 K, as characterized by the appearance of distinct additional peaks in the neutron diffraction pattern below T(N). Its magnetic reflections can be indexed with a propagation vector k = (0,0,0). The magnetic moments inside the FeO6-FeO5 clusters are ferromagnetic, whereas these clusters are antiferromagnetic along the chains. The adjacent chains are in turn ferromagnetically arranged along the a-axis. The magnetic structure of Li2FeP2O7 cathode material is described focusing on their localized spin-spin exchange. The magnetic structure and properties have been generalized for Li2FeP2O7-Li2CoP2O7 binary solid solutions.