Next-generation biomedical devices will need to be self-powered and conformable to human skin or other tissue. Such devices would enable the accurate and continuous detection of physiological signals without the need for an external power supply or bulky connecting wires. Self-powering functionality could be provided by flexible photovoltaics that can adhere to moveable and complex three-dimensional biological tissues and skin. Ultra-flexible organic power sources that can be wrapped around an object have proven mechanical and thermal stability in long-term operation, making them potentially useful in human-compatible electronics. However, the integration of these power sources with functional electric devices including sensors has not yet been demonstrated because of their unstable output power under mechanical deformation and angular change. Also, it will be necessary to minimize high-temperature and energy-intensive processes when fabricating an integrated power source and sensor, because such processes can damage the active material of the functional device and deform the few-micrometre-thick polymeric substrates. Here we realize self-powered ultra-flexible electronic devices that can measure biometric signals with very high signal-to-noise ratios when applied to skin or other tissue. We integrated organic electrochemical transistors used as sensors with organic photovoltaic power sources on a one-micrometre-thick ultra-flexible substrate. A high-throughput room-temperature moulding process was used to form nano-grating morphologies (with a periodicity of 760 nanometres) on the charge transporting layers. This substantially increased the efficiency of the organophotovoltaics, giving a high power-conversion efficiency that reached 10.5 per cent and resulted in a high power-per-weight value of 11.46 watts per gram. The organic electrochemical transistors exhibited a transconductance of 0.8 millisiemens and fast responsivity above one kilohertz under physiological conditions, which resulted in a maximum signal-to-noise ratio of 40.02 decibels for cardiac signal detection. Our findings offer a general platform for next-generation self-powered electronics.