The growth, structural and optical properties, and energy band alignments of tensile-strained germanium (ε-Ge) epilayers heterogeneously integrated on silicon (Si) were demonstrated for the first time. The tunable ε-Ge thin films were achieved using a composite linearly graded InxGa1–xAs/GaAs buffer architecture grown via solid source molecular beam epitaxy. High-resolution X-ray diffraction and micro-Raman spectroscopic analysis confirmed a pseudomorphic ε-Ge epitaxy whereby the degree of strain varied as a function of the InxGa1–xAs buffer indium alloy composition. Sharp heterointerfaces between each ε-Ge epilayer and the respective InxGa1–xAs strain template were confirmed by detailed strain analysis using cross-sectional transmission electron microscopy. Low-temperature microphotoluminescence measurements confirmed both direct and indirect bandgap radiative recombination between the Γ and L valleys of Ge to the light-hole valence band, with L-lh bandgaps of 0.68 and 0.65 eV demonstrated for the 0.82 ± 0.06% and 1.11 ± 0.03% strained Ge on Si, respectively. Type-I band alignments and valence band offsets of 0.27 and 0.29 eV for the ε-Ge/In0.11Ga0.89As (0.82%) and ε-Ge/In0.17Ga0.83As (1.11%) heterointerfaces, respectively, show promise for ε-Ge carrier confinement in future nanoscale optoelectronic devices. Therefore, the successful heterogeneous integration of tunable tensile-strained Ge on Si paves the way for the design and implementation of novel Ge-based photonic devices on the Si technology platform.