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The GaAs-based material system is well-known for hosting InAs quantum dots (QDs) with outstanding optical properties, typically emitting at a wavelength of around 900 nm. The insertion of a metamorphic buffer (MMB) can shift this emission to the technologically attractive telecom C-band range centered at 1550 nm. However, the thickness of common MMB designs (>1 μm) limits their compatibility with most photonic resonator types. Here, we report on the metal–organic vapor-phase epitaxy (MOVPE) growth of a novel InGaAs MMB with a nonlinear indium content grading profile designed to maximize plastic relaxation within minimal layer thickness. This allows us to achieve the necessary transition of the lattice constant and to provide a smooth surface for QD growth within 180 nm. Single-photon emission at 1550 nm from InAs QDs deposited on top of this thin-film MMB is demonstrated. The strength of the new design is proven by integrating it into a bullseye cavity via nano-structuring techniques. The presented advances in the epitaxial growth of QD/MMB structures form the basis for the fabrication of high-quality telecom nonclassical light sources as a key component of photonic quantum technologies.