The exchange bias effect has been studied in Ni/NiO nanogranular samples prepared by mechanical milling and partial hydrogen reduction of NiO; the Ni weight fraction varied between 4% and 69%. In this procedure, coarse-grained NiO powder has been ball-milled in air for 20 hours and subsequently subjected to annealing in H2 (at a temperature ranging between 200 °C and 300 °C) to induce the formation of metallic Ni. The structural properties of the samples have been studied by X-ray diffraction, electron microscopy and extended X-ray absorption fine structure. The magnetic properties have been extensively investigated by carrying out hysteresis loops and magnetization measurements in the 5-300 K temperature range, in zero-field-cooling and field-cooling conditions. The results indicate that both in the as-milled NiO powder and in the hydrogenated samples, the NiO phase is composed of nanocrystallites (having a mean size of ~ 20 nm, structurally and magnetically ordered) and of highly disordered regions. The samples with low Ni content (up to 15%) can be modeled as a collection of Ni nanoparticles (mean size of ~ 10 nm) dispersed in the NiO phase; with increasing the Ni content, the Ni nanoparticles slightly increase in size and tend to arrange in agglomerates. In the Ni/NiO samples, the exchange field depends on the Ni amount, being maximum (~ 600 Oe), at T = 5 K, in the sample with 15% Ni. However, exchange bias is observed also in the as-milled NiO powder, despite the absence of metallic Ni. In all the samples, the exchange bias effect vanishes at ~ 200 K. We propose a mechanism for the phenomenon based on the key role of the disordered NiO component, showing a glassy magnetic character. The exchange bias effect is originated by the exchange interaction between the Ni ferromagnetic moments and the spins of the disordered NiO component (in the as-milled NiO powder, the existence of ferromagnetic moments has been connected to chemical inhomogeneities of the NiO phase). The thermal dependence of the exchange bias effect reflects the variation of the anisotropy of the NiO disordered component with temperature.