Individual brains vary in both anatomy and functional organization, even within a given species. Inter-individual variability is a major impediment when trying to draw generalizable conclusions from neuroimaging data collected on groups of subjects. Current co-registration procedures rely on limited data, and thus lead to very coarse inter-subject alignments. In this work, we present a novel method for inter-subject alignment based on Optimal Transport, denoted as Fused Unbalanced Gromov Wasserstein (FUGW). The method aligns two cortical surfaces based on the similarity of their functional signatures in response to a variety of stimuli, while penalizing large deformations of individual topographic organization.We demonstrate that FUGW is suited for whole-brain landmark-free alignment. The unbalanced feature allows to deal with the fact that functional areas vary in size across subjects. Results show that FUGW alignment significantly increases between-subject correlation of activity during new independent fMRI tasks and runs, and leads to more precise maps of fMRI results at the group level.