Considerable debate surrounds the source of the apparently 'anomalous' increase of atmospheric methane concentrations since the mid-Holocene (5,000 years ago) compared to previous interglacial periods as recorded in polar ice core records. Proposed mechanisms for the rise in methane concentrations relate either to methane emissions from anthropogenic early rice cultivation or an increase in natural wetland emissions from tropical or boreal sources. Here we show that our climate and wetland simulations of the global methane cycle over the last glacial cycle (the past 130,000 years) recreate the ice core record and capture the late Holocene increase in methane concentrations. Our analyses indicate that the late Holocene increase results from natural changes in the Earth's orbital configuration, with enhanced emissions in the Southern Hemisphere tropics linked to precession-induced modification of seasonal precipitation. Critically, our simulations capture the declining trend in methane concentrations at the end of the last interglacial period (115,000-130,000 years ago) that was used to diagnose the Holocene methane rise as unique. The difference between the two time periods results from differences in the size and rate of regional insolation changes and the lack of glacial inception in the Holocene. Our findings also suggest that no early agricultural sources are required to account for the increase in methane concentrations in the 5,000 years before the industrial era.