Room‐temperature, high‐sensitivity, and broadband photodetection up to the shortwave infrared (SWIR) region is extremely significant for a wide variety of optoelectronic applications, including contamination identification, thermal imaging, night vision, agricultural inspection, and atmospheric remote sensing. Small‐bandgap semiconductor‐based SWIR photodetectors generally require deep cooling to suppress thermally generated charge carriers to achieve increased sensitivity. Meanwhile, the photogating effect can provide an alternative way to achieve superior photosensitivity without the need for cooling. The optical photogating effect originates from charge trapping of photoinduced carriers at defects or interfaces, resulting in an extremely high photogain (106 or higher). Here, a highly sensitive SWIR hybrid photodetector, fabricated by integrating an organic charge transfer complex on a graphene transistor, is reported. The organic charge transfer complex (tetrathiafulvalene–chloranil) has an exceptional low‐energy intermolecular electronic transition down to 0.5 eV, with the aim of achieving efficient SWIR absorption for wavelengths greater than 2 µm. The photogating effect at the organic complex and graphene interface enables an extremely high photogain and a high detectivity of ≈1013 Jones, along with a response time of 8 ms, at room temperature for a wavelength of 2 µm.