The future ice dynamical contribution to sea level rise (SLR) from 199 ice shelf nourishing drainage basins of the Antarctic Peninsula Ice Sheet is simulated, using the British Antarctic Survey Antarctic Peninsula Ice Sheet Model. Simulations of the grounded ice sheet include response to ice shelf collapse, estimated by tracking thermal ice shelf viability limits in 14 Intergovernmental Panel on Climate Change global climate models ensemble temperature projections. Grounding line retreat in response to ice shelf collapse is parameterized with a new multivariate linear regression model utilizing a range of glaciological and geometric predictor variables. Multimodel means project SLR up to 9.4 mm sea level equivalent (SLE) by 2200, and up to 19 mm SLE by 2300. Rates of SLR from individual drainage basins throughout the peninsula are similar to 2100, yet diverge between 2100 and 2300 due to individual basin characteristics. Major contributors to SLR are the outlet glaciers feeding southern George VI Ice Shelf, accounting for >75% of total SLR in some model runs. Ice sheet thinning induced by ice-shelf removal is large (up to ∼500 m), especially in Palmer Land in the southern Antarctic Peninsula, and may propagate as far as 135 km inland. These results emphasize the importance of the ice dynamical contribution to future sea level of the APIS on decadal to centennial timescales.