For about the last 30 years it has been recognized that the high frequency component of the tree rings 14 C/ 12 C record is dominated by the modulation of the cosmic ray flux by the solar wind. In particular, it has been demonstrated that the three most recent periods of low sunspot occurrence were characterized by high values of atmospheric 14 C/ 12 C. During the last millennium other periods of high 14 C/ 12 C values were observed but their solar origin is still debatable. In the present work we compare these fluctuations with an independent record of cosmogenic 10 Be measured in ice from the South Pole to check the solar origin of the observed 14 C/ 12 C variations. In order to compare quantitatively the results obtained on 10 Be and 14 C, it is necessary to take into account the different behaviour of these two cosmogenic isotopes, and especially the damping effect of the carbon cycle in the case of 14 C. As an input to a 12-box numerical model we used the relative fluctuations of the 10 Be concentrations record measured in South Pole ice and converted it into a synthetic 14 C record. We took into account the fact that 10 Be modulation is enhanced in polar regions due to the orientation of the geomagnetic field. As expected, the fluctuations of the modelled 14 C record are much smaller (a factor of 20) than those observed for the raw 10 Be record. In addition, the variations are smoother and shifted in time by a few decades. The 10 Be-based 14 C variations closely resemble the 14 C measurements obtained on tree rings (R = 0.81). In particular, it is easy to identify periods of maximal 14 C/ 12 C which correspond to solar activity minima centred at about 1060, 1320 (Wolf), 1500 (Spörer), 1690 (Maunder) and 1820 (Dalton) yr A.D. Cross-correlation calculations suggest that there is no significant lag between the 10 Be-based 14 C and the tree-ring 14 C records. Our study strongly suggests the dominance of the solar modulation on the cosmonuclide production variations during the last millennium.