Debris-covered glaciers are common in rapidly-eroding alpine landscapes. When thicker than a few centimeters, surface debris suppresses melt rates. If continuous debris cover is present, mass balance gradients can be reduced leading to increases in glacier length. In order to quantify feedbacks in the debris-glacier-climate system, we developed a 2-D long-valley numerical glacier model that includes englacial and supraglacial advection. We ran 120 simulations in which a steady state debris-free glacier responds to a step increase of surface debris deposition. Simulated glaciers advance to steady states in which ice accumulation equals ice ablation, and debris input equals debris loss from the glacier. Our model and parameter selections produce two-fold increases in glacier length. Debris flux onto the glacier and the relationship between debris thickness and melt rate strongly control glacier length. Debris deposited near the equilibrium-line altitude, where ice discharge is high, results in the greatest glacier extension when other debris related variables are held constant. Continuous debris cover reduces ice discharge gradients, ice thickness gradients, and velocity gradients relative to initial debris-free glaciers. Debris-forced glacier extension decreases the ratio of accumulation zone to total glacier area (AAR). The model reproduces first-order relationships between debris cover, AARs, and glacier surface velocities from glaciers in High Asia. We provide a quantitative, theoretical foundation to interpret the effect of debris cover on the moraine record, and to assess the effects of climate change on debris-covered glaciers.