Glacial varves can give significant insights into recession and melting rates of decaying ice sheets. Moreover, varve chronologies can provide an independent means of comparison to other annually resolved climatic archives, which ultimately help to assess the timing and response of an ice sheet to changes across rapid climate transitions. Here we report a composite 1257‐year‐long varve chronology from southeastern Sweden spanning the regional late Allerød–late Younger Dryas pollen zone. The chronology was correlated to the Greenland Ice‐Core Chronology 2005 using the time‐synchronous Vedde Ash volcanic marker, which can be found in both successions. For the first time, this enables secure placement of the Lateglacial Swedish varve chronology in absolute time. Geochemical analysis from new varve successions indicate a marked change in sedimentation regime accompanied by an interruption of ice‐rafted debris deposition synchronous with the onset of Greenland Stadial 1 (GS‐1; 12 846 years before AD 1950). With the support of a simple ice‐flow/calving model, we suggest that slowdown of sediment transfer can be explained by ice‐sheet margin stabilization/advance in response to a significant drop of the Baltic Ice Lake level. A reassessment of chronological evidence from central‐western and southern Sweden further supports the hypothesis of synchronicity between the first (penultimate) catastrophic drainage of the Baltic Ice Lake and the start of GS‐1 in Greenland ice‐cores. Our results may therefore provide the first chronologically robust evidence linking continental meltwater forcing to rapid atmosphere–ocean circulation changes in the North Atlantic.