On‐chip stimulated Brillouin scattering (SBS) in arsenic trisulfide (As2S3) planar waveguides lead to a range of outstanding demonstrations in microwave photonics signal generation and processing. However, the lack of other integrated functionalities, high back reflections, and large in‐ and out‐fiber coupling losses in high index contrast waveguides cause a number of serious impairments and lessen the applicability of microwave photonic devices. In this report, a hybrid integration scheme is demonstrated where As2S3 waveguides optimized for SBS gain are coupled with very low losses via a vertical taper to a high index contrast and versatile germanosilicate (Ge:SiO2) platform. The Ge:SiO2 waveguide is optimally mode‐matched to commercially available high numerical aperture optical fiber to achieve very low coupling losses. The structure has very low back reflection due to the adiabatic nature of the taper and negligible refractive index difference across the fiber‐chip interface. The hybrid architecture exhibits a similar Brillouin gain coefficient to its monolithic counterpart but with an improvement of >3 dB/facet fiber‐to‐chip loss and >20 dB reduction in facet reflectivity. The hybrid structures demonstrated will bring chalcogenide‐based chip scale SBS devices closer to practical application.