The effect of the North Atlantic Ocean on the Greenland Ice Sheet through submarine melting of Greenland's tidewater glacier calving fronts is thought to be a key driver of widespread glacier retreat, dynamic mass loss and sea level contribution from the ice sheet. Despite its critical importance, problems of process complexity and scale hinder efforts to represent the influence of submarine melting in ice-sheet-scale models. Here we propose parameterizing tidewater glacier terminus position as a simple linear function of submarine melting, with submarine melting in turn estimated as a function of subglacial discharge and ocean temperature. The relationship is tested, calibrated and validated using datasets of terminus position, subglacial discharge and ocean temperature covering the full ice sheet and surrounding ocean from the period 1960–2018. We demonstrate a statistically significant link between multi-decadal tidewater glacier terminus position change and submarine melting and show that the proposed parameterization has predictive power when considering a population of glaciers. An illustrative 21st century projection is considered, suggesting that tidewater glaciers in Greenland will undergo little further retreat in a low-emission RCP2.6 scenario. In contrast, a high-emission RCP8.5 scenario results in a median retreat of 4.2 km, with a quarter of tidewater glaciers experiencing retreat exceeding 10 km. Our study provides a long-term and ice-sheet-wide assessment of the sensitivity of tidewater glaciers to submarine melting and proposes a practical and empirically validated means of incorporating ocean forcing into models of the Greenland ice sheet.