Intensive efforts have been devoted to the exploration of new optoelectronic devices based on two-dimensional transition-metal dichalcogenides (TMDCs) owing to their strong light-matter interaction and distinctive material properties. In particular, photodetectors featuring both high-speed and high-responsivity performance are of great interest for a vast number of applications such as high-data-rate interconnects operated at standardized telecom wavelengths. Yet, the intrinsically small carrier mobilities of TMDCs become a bottleneck for high-speed application use. Here, we present high-performance vertical van der Waals heterostructure-based photodetectors integrated on a silicon photonics platform. Our vertical MoTe2-graphene heterostructure design minimizes the carrier transit path length in TMDCs and enables a record-high measured bandwidth of at least 24 GHz under a moderate bias voltage of -3 V. Applying a higher bias or employing thinner MoTe2 flakes boosts the bandwidth even to 50 GHz. Simultaneously, our device reaches a high external responsivity of 0.2 A W-1 for incident light at 1,300 nm, benefiting from the integrated waveguide design. Our studies shed light on performance trade-offs and present design guidelines for fast and efficient devices. The combination of two-diemensional heterostructures and integrated guided-wave nano photonics defines an attractive platform to realize high-performance optoelectronic devices, such as photodetectors, light-emitting devices and electro-optic modulators.