Understanding historical and projected coastal sea-level change is limited because the impact of large-scale ocean dynamics is not well constrained. Here, we use a global set of tide-gauge records over nine regions to analyse the relationship between coastal sea-level variability and open-ocean steric height, related to density fluctuations. Interannual-to-decadal sea-level variability follows open-ocean steric height variations along many coastlines. We extract their common modes of variability and reconstruct coastal sterodynamic sea level, which is due to ocean density and circulation changes, based on steric height observations. Our reconstruction, tested in Earth system models, explains up to 91% of coastal sea-level variability. Combined with barystatic components related to ocean mass change and vertical land motion, the reconstruction also permits closure of the coastal sea-level budget since 1960. We find ocean circulation has dominated coastal sea-level budgets over the past six decades, reinforcing its importance in near-term predictions and coastal planning. Coastal sea levels are impacted by local vertical land motion plus local and remote changes to ocean circulation, density and mass changes. Tide-gauge records are used to reconstruct the coastal sea-level budget over nine regions, showing its variability has been dominated by ocean circulation since 1960.