Large amounts of the carbon-isotope ¹⁴C, entering Earth’s carbon cycle, were produced in the atmosphere by atomic bomb tests in the 1950s and 1960s. Here, we forced the ocean and land components of the Community Earth System Model with atmospheric ¹⁴CO₂ over the historical period to constrain overturning time scales and fluxes. The uptake of bomb ¹⁴C by the land model is lower than observation-based estimates. This mismatch is likely linked to too low ¹⁴C uptake by vegetation as the model overestimates ¹⁴C/C ratios of modern soils indicating model biases in forest productivity or wood carbon allocation and turnover. The ocean model matches the observation-based global bomb ¹⁴C inventories when applying the Large and Yeager wind data and the quadratic relationship between gas transfer piston velocity and wind speed of Wanninkhof, 2014. However, ocean bomb ¹⁴C inventories are underestimated in simulations with winds from the Japanese Reanalysis Project, calling for an upward revision of the piston velocity by 15% for this wind product. The sum of ocean, land, and atmospheric bomb ¹⁴C inventory changes is lower in the 1960s than reconstructed bomb ¹⁴C production, likely due to uncertainties in the observational production and atmospheric records and too low land model ¹⁴C uptake. Simulated natural radiocarbon ages in the deep ocean are many centuries older than data-based estimates, indicating too slow deep ocean ventilation. Our study suggests that ¹⁴C observations are key to constrain carbon fluxes and transport timescales within Earth system models.