How does the organisation of neural information-processing enable humans’ sophisticated cognition? Here we decompose functional interactions between brain regions into synergistic and redundant components, revealing their distinct information-processing roles. Combining functional and structural neuroimaging with meta-analytic results, we demonstrate that redundant interactions are predominantly associated with structurally-coupled, modular sensorimotor processing. Synergistic interactions instead support integrative processes and complex cognition across higher-order brain networks. The human brain leverages synergistic information to a greater extent than non-human primates, with high-synergy association cortices exhibiting the highest degree of evolutionary cortical expansion. Synaptic density mapping from Positron Emission Tomography and convergent molecular and metabolic evidence demonstrate that synergistic interactions are supported by receptor diversity and human-accelerated genes underpinning synaptic function. This information-resolved approach provides analytic tools to disentangle information integration from coupling, enabling richer, more accurate interpretations of functional connectivity, and illuminating how the human neurocognitive architecture navigates the trade-off between robustness and integration.