Interactions across the frontal cortex are critical for cognition. Animal studies suggest a role for mediodorsal thalamus (MD) in these interactions, but the computations performed and direct relevance to human reasoning are unclear. Here, inspired by animal work, we build a neural model to derive computational insights and find consistent evidence in fMRI data of humans performing the same probabilistic reversal learning task. We used a reservoir recurrent neural network as a model of the dorso-lateral prefrontal cortex (dlPFC) and found that adding an MD layer with multiplicative inputs to dlPFC supports flexible learning and behavioral switching. In addition, we found a novel computational mechanism where the dlPFC-MD interactions enable the circuit to integrate inputs from other frontal regions, such as the orbitofrontal cortex (OFC), to coordinate the selection of behavioral strategy. Model simulations revealed that integrating votes on behavioral strategy was dependent on an intact MD, and routing votes to MD, rather than dlPFC, required far fewer parameters. Human fMRI data supported these predictions and demonstrated activity from OFC routed to the MD thalamus, when human participants switched behavioral strategies. Collectively, our findings reveal a thalamic role in flexible representations and routing of abstract task information across frontal cortical areas in the human brain.