Molecular hydrogen production occurs through the serpentinization of mantle peridotite exhumed at mid-ocean ridges. Hydrogen is considered essential to sustain microbial life in the subsurface; however, estimates of hydrogen flux through geological time are unknown. Here we present a model of the primary, abiotic production of molecular hydrogen from the serpentinization of oceanic lithosphere using full-plate tectonic reconstructions for the last 200 Ma. We find significant variability in hydrogen fluxes (1-70 • 10¹⁶ mol/Ma or 0.2-14.1 • 10⁵ Mt/a), which are a function of the sensitivity of evolving ocean basins to spreading rates and can be correlated with the opening of key ocean basins during the breakup of Pangea. We suggest that the primary driver of this hydrogen flux is the continental reconfiguration during Pangea breakup, as this produces ocean basins more conducive to exhuming and exposing mantle peridotite at slow and ultraslow spreading ridges. Consequently, present-day flux estimates are ~7 • 10¹⁷ mol/Ma (1.4 • 10⁶ Mt/a), driven primarily by the slow and ultraslow spreading ridges in the Atlantic, Indian, and Arctic oceans. As methane has also been sampled alongside hydrogen at hydrothermal vents, we estimate the methane flux using methane-to-hydrogen ratios from present-day hydrothermal vent fluids. These ratios suggest that methane flux ranges between 10 and 100% of the total hydrogen flux, although as the release of methane from these systems is still poorly understood, we suggest a lower estimate, equivalent to around 7-12 • 10¹⁶ mol/Ma (1.1-1.9 • 10⁷ Mt/Ma) of methane.