Topological superconductivity is an exotic state of matter that supports Majorana zero-modes, which are surface modes in 3D, edge modes in 2D or localized end states in 1D. In the case of complete localization these Majorana modes obey non-Abelian exchange statistics making them interesting building blocks for topological quantum computing. Here we report superconductivity induced into the edge modes of semiconducting InAs/GaSb quantum wells, a two-dimensional topological insulator. Using superconducting quantum interference, we demonstrate gate-tuning between edge-dominated and bulk-dominated regimes of superconducting transport. The edge-dominated regime arises only under conditions of high-bulk resistivity, which we associate with the 2D topological phase. These experiments establish InAs/GaSb as a robust platform for further confinement of Majoranas into localized states enabling future investigations of non-Abelian statistics.