evidence: Variations in solar activity have been proposed to play an important role in recent and past climate change. To study this link on longer timescales, it is essential to know how the Sun has varied over the past millennia. Direct observations of solar variability based on sunspot numbers are limited to the past 400 years, and beyond this we rely on records of cosmogenic radionuclides, such as 14C and 10Be in tree rings and ice cores. Their atmospheric production rates depend on the flux of incoming galactic cosmic rays, which is modulated by Earth’s and the Sun’s magnetic fields, the latter being linked to solar variability. Here we show that accounting for differences in hemispherical production rates, related to geomagnetic field asymmetries, helps resolve so far unexplained differences in Holocene solar activity reconstructions. We find no compelling evidence for long-term variations in solar activity and show that variations in cosmogenic radionuclide production rates on millennial timescales and longer, including the 2,400-year Hallstatt cycle, are explained by variations in the geomagnetic field. Our results also suggest an on-average stronger dipole moment during the Holocene, associated with higher field intensities in the Southern Hemisphere.