Linguistic content can be conveyed both in speech and in writing. But how similar is the neural processing when the same real-life information is presented in spoken and written form? Using functional magnetic resonance imaging, we recorded neural responses from human subjects who either listened to a 7 min spoken narrative or read a time-locked presentation of its transcript. Next, within each brain area, we directly compared the response time courses elicited by the written and spoken narrative. Early visual areas responded selectively to the written version, and early auditory areas to the spoken version of the narrative. In addition, many higher-order parietal and frontal areas demonstrated strong selectivity, responding far more reliably to either the spoken or written form of the narrative. By contrast, the response time courses along the superior temporal gyrus and inferior frontal gyrus were remarkably similar for spoken and written narratives, indicating strong modality-invariance of linguistic processing in these circuits. These results suggest that our ability to extract the same information from spoken and written forms arises from a mixture of selective neural processes in early (perceptual) and high-order (control) areas, and modality-invariant responses in linguistic and extra-linguistic areas.