The geomagnetic dipole moment (GDM) modulates the production rates of cosmogenic radionuclides via the shielding of galactic cosmic rays. Therefore, it is possible to use this linkage to reconstruct past changes in the GDM based on cosmogenic radionuclide records from natural archives such as ice cores. Here we present a GDM reconstruction based on 10Be and 36Cl data from two Greenland ice cores from 11.7 ka to 108 ka b2k (before A.D. 2000). We find that the cosmogenic radionuclide records reflect a mixture of climate and production effects that require separation to evaluate the changes in the GDM. To minimize climate-related variations on isotope data, we applied a multi-linear correction method by removing common variability between 10Be and 36Cl and climate parameters (accumulation rates, δ18O and ion data) from radionuclide records. The resulting “climate corrected” radionuclide data are converted to GDM using a theoretical production model. Comparison of “climate corrected” radionuclides based GDM reconstructions with independent paleomagnetic-derived GDM records shows a good agreement. Furthermore, the “climate correction” leads to an improved agreement with GDM reconstructions than simply using radionuclide fluxes, lending support to the validity of our correction method to isolate production rate changes from ice core radionuclide records. With this correction method, we can extend the GDM reconstructions based on the cosmogenic radionuclides in ice cores to a period when there is a strong climate signal in the data.