The term ‘temporal discounting’ describes both choice preferences and motivation for delayed rewards. Here we show that neuronal activity in the dorsal part of the primate caudate head (dCDh) signals the temporally discounted value needed to compute the motivation for delayed rewards. Macaque monkeys performed an instrumental task, in which visual cues indicated the forthcoming size and delay duration before reward. Single dCDh neurons represented the temporally discounted value without reflecting changes in the animal’s physiological state. Bilateral pharmacological or chemogenetic inactivation of dCDh markedly distorted the normal task performance based on the integration of reward size and delay, but did not affect the task performance for different reward sizes without delay. These results suggest that dCDh is involved in encoding the integrated multidimensional information critical for motivation.