The recent decades of accelerating mass loss of the Greenland ice sheet have arisen from an increase in both surface meltwater runoff and ice flow discharge from tidewater glaciers. Despite the role of the Greenland ice sheet as the dominant individual cryospheric contributor to sea level rise in recent decades, no observational record of its mass loss spans the 30-year period needed to assess its climatological state. We present for the first time a 40-year (1975-2014) time series of observed meltwater discharge from a >6500-km2 catchment of the southwestern Greenland ice sheet. We find that an abrupt 80% increase in runoff occurring between the 1976-2002 and 2003-2014 periods is due to a shift in atmospheric circulation, with meridional exchange events occurring more frequently over Greenland, establishing the first observation-based connection between ice sheet runoff and climate change.