Tannic acid–acetic acid is proposed as novel and green chemicals for cobalt and lithium recycling from spent lithium-ion batteries through a leaching process. The synergism of both acids was documented through batch and continuous studies. Tannic acid promotes cobalt dissolution by reducing insoluble Co3+ into soluble Co2+, while acetic acid is critical to improve the dissolution and stabilize the metals in the pregnant leach solution. Based on batch studies, the optimum conditions for metal recovery at room temperature are acetic acid 1 M, tannic acid 20 g/L, pulp density 20 g/L, and stirring speed 250 rpm (94% cobalt and 99% lithium recovery). The kinetic study shows that increasing temperature to 80 °C improves cobalt and lithium recovery from 65 to 90% (cobalt) and from 80 to 99% (lithium) within 4 h at sub-optimum condition (tannic acid 10 g/L). Kinetic modeling suggests the leaching process was endothermic, and high activation energy indicates a surface chemical process. For other metals, the pattern of manganese and nickel recovery trend follows the cobalt recovery trend. Copper recovery was negatively affected by tannic acid. Iron recovery was limited due to the weak acidic condition of pregnant leach solution, which is beneficial to improve leaching selectivity.