Layered two-dimensional materials have shown novel optoelectronic properties and are well suited to be integrated in planar photonic circuits. For example, graphene has been utilized for wideband photodetection. Because graphene lacks a band gap, however, graphene photodetectors suffer from very high dark current. In contrast, layered black phosphorous, the latest addition to the family of 2D materials, is well-suited for photodetector applications due to its narrow but finite band gap. Here, we demonstrate a gated multilayer black phosphorus photodetector integrated on a silicon photonic waveguide operating in the near-infrared telecom band. In a significant advantage over graphene devices, black phosphorus photodetectors can operate under a bias with very low dark current and attain intrinsic responsivity up to 135 mA/W and 657 mA/W in 11.5nm and 100 nm thick devices, respectively, at room temperature. The photocurrent is dominated by the photovoltaic effect with a high response bandwidth exceeding 3 GHz.