Perceptual interpretations of the environment emerge from the concerted activity of neural populations in decision-making areas downstream of sensory cortex. When the sensory input is ambiguous, perceptual interpretations can be biased by prior beliefs that reflect knowledge of environmental regularities. These effects are examples of Bayesian reasoning, an inference method in which prior knowledge is leveraged to optimize decisions. However, it is not known how decision-making circuits combine sensory signals and prior beliefs to form a perceptual decision. Here, we study neural population activity in the prefrontal cortex of macaque monkeys trained to report perceptual judgments of ambiguous visual stimuli under different prior statistics. We analyze the component of the neural population response that specifically represents the formation of the perceptual decision (the decision variable, DV), and find that its dynamical evolution reflects the integration of sensory signals and prior beliefs. The DV’s initial value before stimulus onset reflects the prior belief in the future state of the environment, while the dynamic range of the DV’s ensuing excursion reflects the relative influence of the incoming sensory signals. The interaction between both factors is better described by addition than by multiplication. These results reveal a general mechanism by which prefrontal circuits can execute Bayesian inference.