Palm kernel cake (PKC), the residue obtained after extraction of palm oil from oil palm seeds and tamarind seed powder (TSP) obtained after removing the fruit pulp from tamarind fruit pod were tested for the production of tannase under solid-state fermentation (SSF) using Aspergillus niger ATCC 16620. The fungal strain was grown on the substrates without any pretreatment. In PKC medium, a maximum enzyme yield of 13.03 IU/g dry substrate (gds) was obtained when SSF was carried out at 30 °C, 53.5% initial substrate moisture, 33 × 109 spores/5 g substrate inoculum size and 5% tannic acid as additional carbon source after 96 h of fermentation. In TSP medium, maximum tannase yield of 6.44 IU/gds was obtained at 30 °C, 65.75% initial substrate moisture, 11 × 109 spores/5 g substrate inoculum, 1% glycerol as additional carbon source and 1% potassium nitrate as additional nitrogen source after 120 h of fermentation. Results from the study are promising for the economic utilization and value addition of these important agro residues, which are abundantly available in many tropical and subtropical countries.