Using an Earth system model, we simulate stratospheric aerosol injection (SAI) on top of the Representative Concentration Pathways 8.5 future scenario. Our idealized method prescribes aerosol concentration, linearly increasing from 2020 to 2100, and thereafter remaining constant until 2200. In the aggressive scenario, the model projects a cooling trend toward 2100 despite warming that persists in the high latitudes. Following SAI termination in 2100, a rapid global warming of 0.35 K yr−1 is simulated in the subsequent 10 years, and the global mean temperature returns to levels close to the reference state, though roughly 0.5 K cooler. In contrast to earlier findings, we show a weak response in the terrestrial carbon sink during SAI implementation in the 21st century, which we attribute to nitrogen limitation. The SAI increases the land carbon uptake in the temperate forest‐, grassland‐, and shrub‐dominated regions. The resultant lower temperatures lead to a reduction in the heterotrophic respiration rate and increase soil carbon retention. Changes in precipitation patterns are key drivers for variability in vegetation carbon. Upon SAI termination, the level of vegetation carbon storage returns to the reference case, whereas the soil carbon remains high. The ocean absorbs nearly 10% more carbon in the geoengineered simulation than in the reference simulation, leading to a ∼15 ppm lower atmospheric CO2 concentration in 2100. The largest enhancement in uptake occurs in the North Atlantic. In both hemispheres' polar regions, SAI delays the sea ice melting and, consequently, export production remains low. In the deep water of North Atlantic, SAI‐induced circulation changes accelerate the ocean acidification rate and broaden the affected area.