Land glacier extent and volume at the northern and southern margins of the Drake Passage have been in a state of dramatic demise since the early 1990s. Here time-varying space gravity observations from the Gravity Recovery and Climate Experiment (GRACE) are combined with Global Positioning System (GPS) bedrock uplift data to simultaneously solve for ice loss and for solid Earth glacial isostatic adjustment (GIA) to Little Ice Age (LIA) cryospheric loading. The present-day ice loss rates are determined to be −26 ± 6 Gt/yr and −41.5 ± 9 Gt/yr in the Southern and Northern Patagonia Ice Fields (NPI+SPI) and Antarctic Peninsula (AP), respectively. These are consistent with estimates based upon thickness and flux changes. Bounds are recovered for elastic lithosphere thicknesses of 35 ≤ h ≤ 70 km and 20 ≤ h ≤ 45 km and for upper mantle viscosities of 4–8 × 1018 Pa s and 3–10 × 1019 Pa s (using a half-space approximation) for NPI+SPI and AP, respectively, using an iterative forward model strategy. Antarctic Peninsula ice models with a prolonged LIA, extending to A.D. 1930, are favored in all χ2 fits to the GPS uplift data. This result is largely decoupled from Earth structure assumptions. The GIA corrections account for roughly 20–60% of the space-determined secular gravity change. Collectively, the on-land ice losses correspond to volume increases of the oceans equivalent to 0.19 ± 0.045 mm/yr of sea level rise for the last 15 years.