Quantum dots (QDs) can act as convenient hosts of two-level quantum szstems, such as single electron spins, hole spins or excitons (bound electron-hole pairs). Due to quantum confinement, the ground state of a single hole confined in a QD usually has dominant heavy-hole (HH) character. For this reason light-hole (LH) states have been largely neglected, despite the fact that may enable the realilzation of coherent photon-to-spin converters or allow for faster spin manipulation compared to HH states. In this work, we use tensile strains larger than 0.3% to switch the ground state of excitons confined in high quality GaAs/AlGaAs QDs from the conventional HH- to LH-type. The LH-exciton fine structure is characterized by two in-plane-polarized lines and, ~400 micro-eV above them, by an additional line with pronounced out-of-plane oscillator strength, consistent with theoretical predictions based on atomistic empirical pseudopotential calculations and a simple mesoscopic model.