This paper introduces the concept of "climate matching" as a driver of migration and establishes several new results. First, we show that climate strongly predicts the spatial distribution of immigrants in the US, both historically (1880) and more recently (2015), whereby movers select destinations with climates similar to their place of origin. Second, we analyze historical flows of German, Norwegian, and domestic migrants in the US and document that climate sorting also holds within countries. Third, we exploit variation in the long-run change in average US climate from 1900 to 2019 and find that migration increased more between locations whose climate converged. Fourth, we verify that results are not driven by the persistence of ethnic networks or other confounders, and provide evidence for two complementary mechanisms: climate-specific human capital and climate as amenity. Fifth, we back out the value of climate similarity by: i) exploiting the Homestead Act, a historical policy that changed relative land prices; and, ii) examining the relationship between climate mismatch and mortality. Finally, we project how climate change shapes the geography of US population growth by altering migration patterns, both historically and into the 21st century.