The composting process of organic fraction of municipal solid waste, besides to the residual compost, generates a wastewater that is characterized by a high organic load. The application of anaerobic processes represents an advantageous solution for the treatment and valorization of this type of wastewater. Nevertheless, few works have been focused on the anaerobic digestion of compost leachate. To overcome this dearth, in the present paper an extensive experimental investigation was carried out to develop and analyse the anaerobic treatment of young leachate in completely stirred tank reactors (CSTR). Initially, it was defined a suitable leachate pretreatment to correct its acidic characteristics that is potentially able to inhibit methanogenic biomass activity. The pretreated leachate was fed to the digester over the start-up phase that was completed in about 40 days. During the operational period, the organic load rate (OLR) changed between 4.25 kgCOD/m3d and 38.5 kgCOD/m3d. The chemical oxygen demand (COD) abatement was higher than 90% for OLR values up to 14.5 kgCOD/m3d and around to 80% for applied loads equal to 24.5 kgCOD/m3d. At this OLR, it was reached the maximum daily biogas production of about 9.3 Lbiogas/(Lreactord). The CH4 fraction was between 70%−78% and the methane production yield in the range 0.34−0.38 LCH4/gCODremoved. The deterioration of biogas production started for OLR values that were over the threshold of 24.5 kgCOD/m3d when a volatile fatty acids (VFA) accumulation occurred and the pH dropped below 6.5. The maximum ratio between VFA and alkalinity (ALK) tolerable in the CSTR was identified to be 0.5 gCH3COOH/gCaCO3. Through an economic analysis, it was proven that the digestion of compost leachate could ensure significant economic profits. Furthermore, the produced digestate had characteristics that were compatible for agricultural applications.