Rapid growth of stretchable electronics stimulates broad uses in multidisciplinary fields as well as industrial applications. However, existing technologies are unsuitable for implementing versatile applications involving adaptable system design and functions in a cost/time-effective way because of vacuum-conditioned, lithographically-predefined processes. Here, we present a methodology for a fully printable, strain-engineered electronic wrap as a universal strategy which makes it more feasible to implement various stretchable electronic systems with customizable layouts and functions. The key aspects involve inkjet-printed rigid island (PRI)-based stretchable platform technology and corresponding printing-based automated electronic functionalization methodology, the combination of which provides fully printed, customized layouts of stretchable electronic systems with simplified process. Specifically, well-controlled contact line pinning effect of printed polymer solution enables the formation of PRIs with tunable thickness; and surface strain analysis on those PRIs leads to the optimized stability and device-to-island fill factor of strain-engineered electronic wraps. Moreover, core techniques of image-based automated pinpointing, surface-mountable device based electronic functionalizing, and one-step interconnection networking of PRIs enable customized circuit design and adaptable functionalities. To exhibit the universality of our approach, multiple types of practical applications ranging from self-computable digital logics to display and sensor system are demonstrated on skin in a customized form.