Using a recently developed 1/12th degree regional ocean model, we establish a link between U.S. East Coast sea level variability and offshore upper-ocean heat content change. This link manifests as a cross-shore mass redistribution driven by an offshore thermosteric sea level response to subsurface warming or cooling. Approximately 50\% of simulated monthly to inter-annual coastal sea level variance south of Cape Hatteras can be statistically accounted for by this mechanism, realized as a function of regional ocean hypsometry, gyre scale warming, and the depth-dependence of density change. This response to offshore warming explains the non-stationarity of U.S. East coast sea level covariance, specifically observed and modeled behavior after $\sim$ 2010. Since approximately 2010, elevated rates of sea level rise south of Cape Hatteras can be partly explained as the result of shore-ward mass redistribution due to offshore sub-surface warming within the North Atlantic subtropical gyre. These results reveal a mechanism that connects local coastal sea level to a broader region and identifies the influence of regional heat content changes on coastal sea level. This analysis presents a framework for identifying new regions that may be susceptible to enhanced sea level rise due to ocean warming and helps bridge the gap between quantifying large scale change and anticipating local coastal impacts like flooding and storm surge.