The distribution and atmospheric budgets for molecular hydrogen and its deuterium component δD are simulated with the GEOS-Chem global chemical transport model and constrained by observations of H2 from the NOAA Climate Monitoring and Diagnostics Laboratory network and δD observations from ship and ground stations. Our simulation includes a primary H2 source of 38.8 Tg a−1 (22.7 Tg a−1 from fossil and biofuels, 10.1 Tg a−1 from biomass burning, 6.0 Tg a−1 from the ocean) (where a is years) and a secondary photochemical source from photolysis of formaldehyde of 34.3 Tg a−1. The simulated global tropospheric mean H2 is 525 ppbv, with a tropospheric burden of 141 Tg and tropospheric lifetime of 1.9 a. Uptake by enzymes in soils accounts for 75% of the H2 sink, with the remainder due to reaction with OH. The model captures the observed latitudinal, vertical, and seasonal variations of H2. For δD we find that a photochemical source signature from methane and biogenic volatile organic compound oxidation of 162‰ yields a global mean atmospheric δD of 130‰, consistent with atmospheric observations. The model captures the observed latitudinal gradient in δD, simulating a 21‰ greater enrichment in the Southern Hemisphere because of the predominance of isotopically depleted fossil fuel emissions in the Northern Hemisphere. We find that stratospheric-tropospheric exchange results in 37‰ enrichment of tropospheric δD. Our simulation provides new simultaneous constraints on the H2 soil sink (55 ± 8 Tg a−1), the ocean source (6 ± 3 Tg a−1), and the isotopic signature for photochemical production (162 ± 57‰).