Contemporary theories assume that semantic cognition emerges from a neural architecture in which different component processes are combined to produce aspects of conceptual thought and behaviour. In addition to the state-level, momentary variation in brain connectivity, individuals may also differ in their propensity to generate particular configurations of such components, and these trait-level differences may relate to individual differences in semantic cognition. We tested this view by exploring how variation in intrinsic brain functional connectivity between semantic nodes in fMRI was related to performance on a battery of semantic tasks in 154 healthy participants. Through simultaneous decomposition of brain functional connectivity and semantic task performance, we identified distinct components of semantic cognition at rest. In a subsequent validation step, these data-driven components demonstrated explanatory power for neural responses in an fMRI-based semantic localiser task and variation in self-generated thoughts during the resting-state scan. Our findings showed that good performance on harder semantic tasks was associated with relative segregation at rest between frontal brain regions implicated in controlled semantic retrieval and the default mode network. Poor performance on easier tasks was linked to greater coupling between the same frontal regions and the anterior temporal lobe; a pattern associated with deliberate, verbal thematic thoughts at rest. We also identified components that related to qualities of semantic cognition: relatively good performance on pictorial semantic tasks was associated with greater separation of angular gyrus from frontal control sites and greater integration with posterior cingulate and anterior temporal cortex. In contrast, good speech production was linked to the separation of angular gyrus, posterior cingulate and temporal lobe regions. Together these data show that quantitative and qualitative variation in semantic cognition across individuals emerges from variations in the interaction of nodes within distinct functional brain networks.