We demonstrate that open solar flux (Fs, derivable from geomagnetic data) exhibits stronger correlations with atmospheric circulation variations than conventionally-used measures of solar activity. The circulation anomalies are particularly enhanced over the North Atlantic/Eurasian sector, where there are large changes in the occurrence of blocking and the winter mean surface temperature differs by several degrees between high- and low-solar terciles. The relationship is stronger and simpler for Fs, being more linear between high- and low-solar winters. While the circulation anomalies strongly resemble the North Atlantic Oscillation they also extend deeper into Eurasia, especially in high-solar conditions. This distinct signature may be useful for the detection and attribution of observed changes and also the identification of dynamical mechanisms.