Strain and bandgap engineered epitaxial germanium (ε-Ge) quantum-well (QW) laser structures were investigated on GaAs substrates theoretically and experimentally for the first time. In this design, we exploit the ability of InGaAs layer to simultaneously provide tensile strain in Ge (0.7% to 1.96%) and sufficient optical and carrier confinement. The direct band-to-band gain, threshold current density (Jth) and loss mechanisms that dominate in the ε-Ge QW laser structure, were calculated using first-principles-based 30-band k.p electronic structure theory, at injected carrier concentrations from 3x10 18 cm -3 to 9x10 19 cm -3 . The higher strain in ε-Ge QW increases the gain at higher wavelengths; however, a decreasing thickness is required by higher strain due to critical layer thickness for avoiding strain relaxation. In addition, we predict that a Jth of 300 A/cm 2 can be reduced to <10 A/cm 2 by increasing strain from 0.2% to 1.96% in ε-Ge lasing media. The measured room temperature photoluminescence spectroscopy demonstrated direct bandgap optical emission from the conduction band at valley to heavy-hole (0.6609 eV) from 1.6% tensile strained Ge/In0.24Ga0.76As heterostructure grown by molecular beam epitaxy, is in agreement with the value calculated using 30-band k.p