The variations of atmospheric Δ¹⁴C over the past two millennia are classically attributed to changes in its production rate in the upper atmosphere, which in turn is related to changes in solar activity and the Earth's magnetic field. However, the potential contribution of atmospheric and oceanic circulation changes during this period has not been precisely quantified. This has been achieved here using a coupled climate model simulating explicitly the evolution of the different carbon isotopes, driven by a new estimate of ¹⁴C production derived from ¹⁰Be measurements, and using different production rates for each hemisphere. Our results confirm that changes in global and hemispheric atmospheric Δ¹⁴C are primarily driven by changes in production rate. The very good agreement between our results and observed atmospheric Δ¹⁴C also highlights the strong consistency of current interpretations of ¹⁰Be and ¹⁴C measurements. By contrast, the interhemispheric difference in atmospheric Δ¹⁴C is controlled by changes in the intensity of southern hemisphere westerly winds (SHWW) that impact atmosphere-ocean exchange and the upwelling of ¹⁴C depleted water masses in the Southern Ocean. Changes in deep water formation in both hemispheres or open ocean polynyas in the Southern Ocean only have a small impact on atmospheric Δ¹⁴C over that period. When driven by changes in the SHWW proportional to three existing reconstructions of the Southern Annular Mode (SAM) index, the model reproduces some key characteristics of the observed interhemispheric Δ¹⁴C gradient. These include the low values in the 15th century and the peak in the 16th century, but there are also clear differences between the experiments and Δ¹⁴C observations. This suggests that while SAM reconstructions capture some robust features in the centennial variability, large uncertainties remain.