Soft integrated electronics are key components for emerging applications in wearable biomonitoring, soft co-robotics, and physical human-machine interaction. They are composed of soft and elastically deformable circuits and sensors that are combined with packaged microelectronics for signal processing, power regulation, and communication. While promising, widespread use of soft wearable electronics is currently limited by the lack of robust fabrication techniques to rapidly, efficiently, and precisely assemble soft and rigid components into multilayered systems. Here, an efficient digital fabrication approach is presented to create highly customizable wearable electronics through rapid laser machining and adhesion controlled soft materials assembly. Well aligned, multilayered materials are created from 2D and 3D elements that stretch and bend while seamlessly integrating with rigid components such as microchip integrated circuits, discrete electrical components, and interconnects. These techniques are applied using commercially available materials and components and the fabrication of thin, lightweight, customized sensor skins is demonstrated in under an hour. These fully integrated wireless devices conformably bond to the hand and are successfully used for monitoring hand gesture, pulse rate, and blood oxygenation. These materials and methods enable custom wearable electronics while offering versatility in design and functionality for a variety of applications through material selection and construction.