Humans value rewards less when these are delivered in the future as opposed to immediately, a phenomenon referred to as delay discounting. While delay discounting has been studied during the anticipation of rewards and in the context of intertemporal decision-making, little is known about its neural correlates in the outcome phase (during reward delivery) and their relation to personality. Personality traits that have been associated with increased delay discounting include impulsivity and, potentially, anxious-depressive traits. Here we performed functional magnetic resonance imaging (fMRI) in 72 healthy participants while they carried out a monetary incentive delay (MID) task with a delay manipulation. In sixty percent of the experimental trials, participants won rewards that differed in magnitude (0.05€, 0.50€ or 1€) and delay until delivery (immediately, 10 days, or 100 days). A factor analysis on questionnaires yielded two factors reflecting Impulsivity and Anxiety/Depression, which we used to examine potential relationships between personality and delay discounting. When winning a reward, medial prefrontal cortex (mPFC) activation was higher for immediate compared to delayed rewards. Moreover, amygdala activation correlated with reward magnitude for immediate but not for delayed rewards. Amygdala activation to winning immediate rewards was higher in more impulsive participants, while mPFC activation to winning immediate rewards was higher in more anxious-depressed participants. Our results uncover neural correlates of delay discounting during reward delivery, and suggest that impulsivity and subclinical anxious-depressive traits are related to stronger neural responses for winning immediate relative to delayed rewards.