Communication between gray matter regions underpins all facets of brain function. To date, progress in understanding large-scale neural communication has been hampered by the inability of current neuroimaging techniques to track signaling at whole-brain, high-spatiotemporal resolution. Here, we use 2.77 million intracranial EEG recordings, acquired following 29,055 single-pulse electrical stimulations in a total of 550 individuals, to study inter-areal communication in the human brain. We found that network communication models---computed on structural connectivity inferred from diffusion MRI---can explain the propagation of direct, focal electrical stimulation through white matter, measured at millisecond time scales. Building on this finding, we show that a parsimonious statistical model comprising structural, functional and spatial factors can accurately and robustly predict cortex-wide effects of brain stimulation (out-of-sample R2=54%). Our work contributes towards the biological validation of concepts in network neuroscience and provides insight into how white matter connectivity shapes inter-areal signaling. We anticipate that our findings will have implications for research on macroscale neural information processing and the design of brain stimulation paradigms.