We investigate the spatiotemporal evolution of radiocarbon (Δ14C) in the ocean over the 21st century under different scenarios for anthropogenic CO2 emissions and atmospheric CO2 and radiocarbon changes using a 3‐D ocean carbon cycle model. Strong decreases in atmospheric Δ14C in the high‐emission scenario result in strong outgassing of 14C over 2050–2100, causing Δ14C spatial gradients in the surface ocean and vertical gradients between the surface and intermediate waters to reverse sign. Surface Δ14C in the subtropical gyres is lower than Δ14C in Pacific Deep Water and Southern Ocean surface water in 2100. In the low‐emission scenario, ocean Δ14C remains slightly higher than in 1950 and relatively constant over 2050–2100. Over the next 20 years we find decadal changes in Δ14C of −30‰ to +5‰ in the upper 2 km of the ocean, which should be detectable with continued hydrographic surveys. Our simulations can help in planning future observations, and they provide a baseline for investigating natural or anthropogenic changes in ocean circulation using ocean Δ14C observations and models.