A striking feature of human perception is that our subjective experience depends not only on sensory information from the environment but also on our prior knowledge or expectations. The precise mechanisms by which sensory information and prior knowledge are integrated remain unclear, with longstanding disagreement concerning whether integration is strictly feedforward or whether higher-level knowledge influences sensory processing through feedback connections. Here we used concurrent EEG and MEG recordings to determine how sensory information and prior knowledge are integrated in the brain during speech perception. We manipulated listeners' prior knowledge of speech content by presenting matching, mismatching, or neutral written text before a degraded (noise-vocoded) spoken word. When speech conformed to prior knowledge, subjective perceptual clarity was enhanced. This enhancement in clarity was associated with a spatiotemporal profile of brain activity uniquely consistent with a feedback process: activity in the inferior frontal gyrus was modulated by prior knowledge before activity in lower-level sensory regions of the superior temporal gyrus. In parallel, we parametrically varied the level of speech degradation, and therefore the amount of sensory detail, so that changes in neural responses attributable to sensory information and prior knowledge could be directly compared. Although sensory detail and prior knowledge both enhanced speech clarity, they had an opposite influence on the evoked response in the superior temporal gyrus. We argue that these data are best explained within the framework of predictive coding in which sensory activity is compared with top-down predictions and only unexplained activity propagated through the cortical hierarchy.