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Although recent progress in the field of flexible electronics has allowed the realization of biocompatible and conformable electronics, systematic approaches which combine high bendability (<3 mm bending radius), high stretchability (>3-4%), and low complexity in the fabrication process are still missing. Here, we show a technique to induce randomly oriented and customized wrinkles on the surface of a biocompatible elastomeric substrate, where Thin-Film Transistors (TFTs) and circuits (inverter and logic NAND gates) based on amorphous-IGZO are fabricated. By tuning the wavelength and the amplitude of the wrinkles, the devices are fully operational while bent to 13 μm bending radii as well as while stretched up to 5%, keeping unchanged electrical properties. Moreover, a flexible rectifier is also realized, showing no degradation in the performances while flat or wrapped on an artificial human wrist. As proof of concept, transparent TFTs are also fabricated, presenting comparable electrical performances to the nontransparent ones. The extension of the buckling approach from our TFTs to circuits demonstrates the scalability of the process, prospecting applications in wireless stretchable electronics to be worn or implanted.