Graphene–silicon (GS) Schottky junctions have been demonstrated as an efficient architecture for photodetection. However, the response speed of such devices for free space light detection has so far been limited to 10s–100s of kHz for wavelength λ >500 nm. Here, we demonstrate GS Schottky junction photodetectors fabricated on a silicon-on-insulator substrate (SOI) with response speeds approaching 1 GHz, attributed to the reduction of the photo-active silicon layer thickness to 10 μm and with it a suppression of speed-limiting diffusion currents. Graphene–silicon-on-insulator photodetectors (GSOI-PDs) exhibit a negligible influence of wavelength on response speed and only a modest compromise in responsivities compared to GS junctions fabricated on bulk silicon. Noise-equivalent-power (NEP) and specific detectivity (D*) of GSOI photodetectors are 14.5 pW and 7.83 × 1010 cm Hz1/2 W−1, respectively, in ambient conditions. We further demonstrate that combining GSOI-PDs with micro-optical elements formed by modifying the surface topography enables engineering of the spectral and angular response.