Animals adapt their behaviour to novel situations, quickly learning to respond appropriately to external stimuli. While different brain areas are thought to make distinct contributions to goal-directed behaviour, it remains unclear how the brain as a network of areas enables goal-directed learning. Here, we developed a behavioural paradigm that allows us to probe rapid reward-based sensorimotor learning in mice, overcoming the limitations of longitudinal recordings. Mice are first pretrained on an auditory detection task and, once expert, are transferred to a whisker-based tactile detection task. First, we observed that mice learn the new whisker-reward association on the timescale of minutes and go from novice to expert performance levels within a single session. Second, this learning is reward-dependent and often requires few trials to emerge. During this single-session learning, we performed brain-wide simultaneous Neuropixels recordings across multiple cortical and subcortical brain areas aligned to a reference atlas. We observed widespread task-related neuronal activity across diverse brain areas beyond those that are typically considered in whisker detection tasks. Further, specific neuronal populations showed reward-dependent changes in representations upon trial-by-trial learning. Our experiments begin to describe the brain-wide dynamics of neuronal activity during minute-timescale learning and future work will investigate changes in inter-areal interactions.