Human learning is a complex process in which future behavior is altered via the modulation of neural activity.   Yet, the degree to which such activity, and its resultant functional connectivity, is constrained across individual subjects and throughout learning remains unknown. Here, we measured brain activity and functional connectivity in a longitudinal experiment in which healthy adult human participants learned the values of novel objects over the course of four days. We assessed the presence of constraints on activity by calculating the Pearson correlation of a region's fMRI BOLD activity time series across pairs of subjects. Similarly, we assessed the presence of constraints on functional connectivity by calculating the Pearson correlation of the functional connectivity of a region across pairs of subjects. Together, these intersubject correlations in activity and connectivity were greater in magnitude than expected in a non-parametric permutation-based null model, particularly in primary sensory and motor systems, as well as in regions associated with the learning of value. Notably, intersubject correlations in activity and connectivity over the whole brain peaked in the early stages of learning, suggesting the presence of strong constraints on early, as opposed to late, skill acquisition. Intersubject correlations in activity were lower in magnitude than intersubject correlations in connectivity later in learning, suggesting that connectivity may be more highly constrained than activity in late skill acquisition. Finally, individual differences in performance accuracy tracked the degree to which a subject's connectivity, but not activity, tracked subject-general constraints. Taken together, our results support the notion that brain activity and connectivity are most constrained across subjects early in learning, with constraints on activity, but not connectivity, decreasing later in learning.