A long-standing task in climate research has been to distinguish between anthropogenic climate change and natural climate variability. A prerequisite for fulfilling this task is the understanding of the relative roles of external drivers and internal variability of climate and the carbon cycle. Here, we present the first ensemble simulations over the last 1200 years with a comprehensive Earth system model including a fully interactive carbon cycle. Applying up-to-date reconstructions of external forcing including the recent low-amplitude estimates of solar variations, the ensemble simulations reproduce temperature evolutions consistent with the range of reconstructions. The 20th-century warming trend stands out against all pre-industrial trends within the ensemble. Volcanic eruptions are necessary to explain variations in pre-industrial climate such as the Little Ice Age; yet only the strongest, repeated eruptions lead to cooling trends that differ significantly from the internal variability across all ensemble members. The simulated atmospheric CO2 concentrations exhibit a stable carbon cycle over the pre-industrial era with multi-centennial variations somewhat smaller than in the observational records. Early land-cover changes have modulated atmospheric CO2 concentrations only slightly. We provide a model-based quantification of the sensitivity (termed gamma) of the global carbon cycle to temperature for a variety of climate and forcing conditions. We diagnose a distinct dependence of gamma on the forcing strength and time-scales involved, thus providing a possible explanation for the systematic difference in the observational estimates for different segments of the last millennium.