The ocean has absorbed anthropogenic carbon dioxide (C_anthro) from the atmosphere and played an important role in mitigating global warming. However, how much C_anthro is accumulated in coastal oceans has rarely been addressed with observational data. The estimation of the coastal C_anthro is challenging due to the lack of robust methods to separate the anthropogenic signal from large natural variations, and the limited availability of long-term high-quality observational data. In this research, we developed regional extended multiple linear regression (eMLR) methods to estimate coastal C_anthro and then validated them using reconstructions of known modeled C_anthro fields from the model output. The validation results demonstrate that the regional eMLR method can capture fine features of C_anthro change (ΔC_anthro) in the North American Coasts with fine resolution. Then we apply this method to a high-quality carbonate dataset (1996-2018) on the U.S. East Coast. From offshore to nearshore, ΔC_anthro decreases with salinity to near zero in the subsurface, indicating no net increase in the export of C_anthro from estuaries and wetlands. Excess ΔC_anthro (relative to a conservative mixing baseline) reveals an uptake of C_anthro from the atmosphere on the shelf. Our analysis suggests that the continental shelf exports most of its C_anthro to the open ocean. Our conclusions may stimulate a community-wide effort to quantify coastal C_anthro accumulation rates as more and more high-quality and long-term carbonate parameter data become available in the highly heterogeneous global coastal oceans in the next two decades, improve the boundary condition constraints in regional and global ocean carbon models, and potentially provide the necessary baseline for assessing the marine carbon dioxide removal (CDR) interventions.