Feedback is a powerful and ubiquitous technique both in classical and quantum system control. Its standard implementation relies on measuring the state of a system, processing the classical signal, and feeding it back to the system. In quantum physics, however, measurements not only read out the state of the system but also modify it irreversibly. Coherent feedback is a different kind of feedback that coherently processes and feeds back quantum signals without actually measuring the system. Here, we report on the experimental realization and the theoretical analysis of an optical coherent feedback platform to control the motional state of a nanomechanical membrane in an optical cavity. The coherent feedback loop consists of a light field interacting twice with the same mechanical mode through different cavity modes, without performing any measurement. Tuning the optical phase and delay of the feedback loop allows us to control the motional state of the mechanical oscillator, its resonance frequency, and also its damping rate, which we use to cool the membrane close to the quantum ground state. Our theoretical analysis provides the optimal cooling conditions, showing that this new technique enables ground-state cooling. Experimentally, we show that we can cool the membrane to a state with n¯m=4.89±0.14 phonons (480 μK) in a 20 K environment. This lies below the theoretical limit of cavity dynamical backaction cooling in the unresolved sideband regime and is achieved with only 1% of the optical power required for cavity cooling. Our feedback scheme is very versatile, offering new opportunities for quantum control in a variety of optomechanical systems.