The out-of-plane integration of microfabricated planar microchips into functional three-dimensional (3D) devices is a challenge in various emerging MEMS applications such as advanced biosensors and flow sensors. However, no conventional approach currently provides a versatile solution to vertically assemble sensitive or fragile microchips into a separate receiving substrate and to create electrical connections. In this study, we present a method to realize vertical magnetic-field-assisted assembly of discrete silicon microchips into a target receiving substrate and subsequent electrical contacting of the microchips by edge wire bonding, to create interconnections between the receiving substrate and the vertically oriented microchips. Vertical assembly is achieved by combining carefully designed microchip geometries for shape matching and striped patterns of the ferromagnetic material (nickel) on the backside of the microchips, enabling controlled vertical lifting directionality independently of the microchip's aspect ratio. To form electrical connections between the receiving substrate and a vertically assembled microchip, featuring standard metallic contact electrodes only on its frontside, an edge wire bonding process was developed to realize ball bonds on the top sidewall of the vertically placed microchip. The top sidewall features silicon trenches in correspondence to the frontside electrodes, which induce deformation of the free air balls and result in both mechanical ball bond fixation and around-the-edge metallic connections. The edge wire bonds are realized at room temperature and show minimal contact resistance (<0.2 Omega) and excellent mechanical robustness (>168mN in pull tests). In our approach, the microchips and the receiving substrate are independently manufactured using standard silicon micromachining processes and materials, with a subsequent heterogeneous integration of the components. Thus, this integration technology potentially enables emerging MEMS applications that require 3D out-of-plane assembly of microchips.