Microresonator devices which possess ultra-high quality factors are essential for fundamental investigations and applications. Microsphere and microtoroid resonators support remarkably high Q's at optical frequencies, while planarity constrains preclude their integration into functional lightwave circuits. Conventional semiconductor processing can also be used to realize ultra-high-Q's with planar wedge-resonators. Still, their full integration with side-coupled dielectric waveguides remains an issue. Here we show the full monolithic integration of a wedge-resonator/waveguide vertically-coupled system on a silicon chip. In this approach the cavity and the waveguide lay in different planes. This permits to realize the shallow-angle wedge while the waveguide remains intact, allowing therefore to engineer a coupling of arbitrary strength between these two. The precise size-control and the robustness against post-processing operation due to its monolithic integration makes this system a prominent platform for industrial-scale integration of ultra-high-Q devices into planar lightwave chips.