In integrated photonics, specific wavelengths are preferred such as 1550 nm due to low-loss transmission and the availability of optical gain in this spectral region. For chip-based photodetectors, layered two-dimensional (2D) materials bear scientific and technologically-relevant properties leading to strong light-matter-interaction devices due to effects such as reduced coulomb screening or excitonic states. However, no efficient photodetector in the telecommunication C-band using 2D materials has been realized yet. Here, we demonstrate a MoTe2-based photodetector featuring strong photoresponse (responsivity = 0.5 A/W) operating at 1550nm on silicon photonic waveguide enabled by engineering the strain (4%) inside the photo-absorbing transition-metal-dichalcogenide film. We show that an induced tensile strain of ~4% reduces the bandgap of MoTe2 by about 0.2 eV by microscopically measuring the work-function across the device. Unlike Graphene-based photodetectors relying on a gapless band structure, this semiconductor-2D material detector shows a ~100X improved dark current enabling an efficient noise-equivalent power of just 90 pW/Hz^0.5. Such strain-engineered integrated photodetector provides new opportunities for integrated optoelectronic systems.