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Taking advantage of the Polar Amplification Model Intercomparison Project simulations and using a Lagrangian objective feature tracking algorithm, we determine the response of extratropical cyclones to sea‐ice loss and consequent weakening of the equator‐to‐pole near‐surface temperature gradient. The wintertime storm tracks are found to shift equatorward in the North Atlantic and over Europe, and eastward in the North Pacific. In both regions, cyclones become weaker and slower, particularly on the poleward flank of the storm tracks. On average, there are fewer individual cyclones in the extratropics each winter, they last longer, are weaker, and travel more slowly. These changes are greatest over the Arctic, but still statistically significant in midlatitudes despite being small compared to internal variability. Inter‐model spread in cyclone responses are not strongly correlated with that in Arctic warming or Arctic amplification. Little change in summertime cyclones is found. Plain Language Summary: Using identically performed experiments from eight different climate models, we study how low pressure systems, known as cyclones or storms, may change as Arctic sea ice diminishes. An algorithm is used to identify the weather systems and track them across their lifecycle. In the wintertime, the typical path of storms over the Atlantic Ocean shifts southward toward the equator. Over the Pacific, the storm tracks shifts toward North America. Arctic sea‐ice loss causes there to be fewer storms each winter across the northern midlatitudes, and these tend to be weaker, slower moving, but longer lasting. These changes are largest over the Arctic itself but also found over mid‐latitudes. These changes may be important because the number, location, and character of storms control the winter weather over Europe, North America and Asia. In the summertime, we did not find any detectable impact of Arctic sea‐ice loss on storms. Key Points: The Northern Hemisphere winter storm tracks shift south and/or east in response to Arctic sea‐ice lossSea ice loss leads to fewer, slower, longer lasting, and weaker wintertime cyclonesResponses are small compared to internal variability, but larger in winter than summer [ABSTRACT FROM AUTHOR]