The Greenland Ice Sheet (GrIS) has experienced sustained mass loss over recent decades in response to Arctic warming, raising concerns about its sensitivity to climate change and its future contribution to sea-level rise. Understanding when and how rapidly the GrIS began to decline provides important constraints on its response to ongoing and future warming. Previous studies have shown that glacier retreat across Greenland began at different times, with some glaciers retreating as early as the mid-19th century and others not until the late 20th century. Although historical evidence (e.g., historical maps, expedition logs) as well as dating of geomorphological features have enabled the reconstruction of ice-front positions for many Greenland glaciers during the 19th and 20th centuries, the timing, magnitude, and spatial distribution of Greenland-wide thinning since the Little Ice Age (LIA,∼1300–1850 CE) remain poorly constrained. Here, we reconstruct Greenland-wide ice surface elevation for 1850 and 1980 using ice-sheet boundaries representative of each period. We generate an ensemble of 127 reconstructions that samples the main sources of uncertainty in past ice-sheet geometry and estimate the spatial distribution of elevation change since 1850. Our reconstruction uses the mass distribution (MD) approach, which combines satellite-era observations of elevation change rates, estimates of total ice-sheet mass change since 1850, and a contemporary digital elevation model to infer past ice-sheet geometry. Using our reconstructed ice-sheet geometries and evolving ice boundaries, we reinterpret existing Greenland-wide mass-change estimates, including those of Mankoff et al. (2021), and obtain a total mass loss equivalent to 26.8 mm SLE between 1850 and 2015 (0.16 mm SLE yr^−1). Of this total, 15.6 mm SLE occurred during 1850–1980 (0.12 mm SLE yr^−1), 5.6 mm during 1980–2007 (0.21 mm SLE yr^−1), and 5.5 mm during 2007–2015 (0.69 mm SLE yr^−1). These results indicate that the average mass-loss rate during 2007–2015 was approximately six times greater than during 1850–1980. Uncertainty of ice surface elevation within the ensemble is primarily controlled by the total ice-sheet mass change since 1850 used to constrain the reconstructions and secondarily by the spatial pattern of observed elevation change rates. Our reconstructions, which explicitly account for historical ice-sheet boundaries, differ substantially from reconstructions based on a contemporary ice mask, highlighting the importance of representing temporal changes in ice extent when reconstructing past Greenland geometry.