The climate varies due to human activity, natural climate cycles, and natural events external to the climate system. Understanding the different roles played by these drivers of variability is fundamental to predicting near-term climate change and changing extremes, and to attributing observed change to anthropogenic or natural factors. Natural drivers such as large explosive volcanic eruptions or multidecadal cycles in ocean circulation occur infrequently and are therefore poorly represented within the observational record. Here we turn to the first high-latitude annually-resolved and absolutely dated marine record spanning the last millennium, and the Paleoclimate Modelling Intercomparison Project (PMIP) Phase 3 Last Millennium climate model ensemble spanning the same time period, to examine the influence of natural climate drivers on Arctic sea ice. We show that bivalve oxygen isotope data are recording multidecadal Arctic sea ice variability and through the climate model ensemble demonstrate that external natural drivers explain up to third of this variability. Natural external forcing causes changes in sea-ice mediated export of freshwater into areas of active deep convection, affecting the strength of the Atlantic Meridional Overturning Circulation (AMOC) and thereby northward heat transport to the Arctic. This in turn leads to sustained anomalies in sea ice extent. The models capture these positive feedbacks, giving us improved confidence in their ability to simulate future sea ice in in a rapidly evolving Arctic.