HgTe-based quantum wells (QWs) recently attracted a lot of attention for the realization of a two-dimensional topological insulator with protected helical edge states. Another class of topological systems are topological superconductors (TSCs) with Majorana edge states. In this paper, we show how proximity induced s-wave superconductivity in the bulk of HgTe-QWs and in the presence of a Zeeman field can exhibit a TSC with chiral Majorana edge states. We calculate the topological invariants and the corresponding Majorana edge states explicitly within a four-band model accounting for inversion symmetry breaking terms due to Rashba spin-orbit coupling and bulk inversion asymmetry present in these QWs.