Branding has become one of the most important determinants of consumer choices. Intriguingly, the psychological mechanisms of how branding influences decision making remain elusive. In the research reported here, we used a preference-based decision-making task and computational modeling to identify which internal components of processing are affected by branding. We found that a process of noisy temporal integration of subjective value information can model preference-based choices reliably and that branding biases are explained by changes in the rate of the integration process itself. This result suggests that branding information and subjective preference are integrated into a single source of evidence in the decision-making process, thereby altering choice behavior.