WTe2 is provoking immense interest owing to its extraordinary properties, such as large positive magnetoresistance, pressure-driven superconductivity and possible type-II Weyl semimetal state. Here we report results of high-pressure synchrotron X-ray diffraction (XRD), Raman and electrical transport measurements on WTe2. Both the XRD and Raman results reveal a structural transition upon compression, starting at 6.0 GPa and completing above 15.5 GPa. We have determined that the high-pressure lattice symmetry is monoclinic 1T' with space group of P21/m. This transition is related to a lateral sliding of adjacent Te-W-Te layers and results in a collapse of the unit cell volume by ∼20.5%. The structural transition also casts a pressure range with the broadened superconducting transition, where the zero resistance disappears.