The connection between the production of the cosmogenic isotope ¹⁰Be and changes in heliomagnetic activity makes ice core ¹⁰Be an attractive proxy for studying changes in solar output. However, interpreting ¹⁰Be ice core records on centennial timescales is complicated by potential climate-related deposition changes that could obscure the ¹⁰Be production signal. By using the Goddard Institute for Space Studies ModelE general circulation model to selectively vary climate and production functions, we model ¹⁰Be flux at key ice-coring sites. We vary geomagnetic field strength and the solar activity modulation parameter (), CO₂, sea surface temperatures, and volcanic aerosols to assess impacts on ¹⁰Be. Specifically, we find significant latitudinal differences in the response of ¹⁰Be fluxes to changes in the production function. In the climate experiments the ¹⁰Be deposition changes simulated over ice sheets in both hemispheres are comparable to those seen in the production experiments. This altered deposition combined with changes of snow accumulation results in significant climate-related ¹⁰Be concentration variation in both Greenland and Antarctica. Over the Holocene our results suggest that the ¹⁰Be response to climate change should not be neglected when inferring production changes.