There are more than 3 million people in the world whose mobility relies on wheelchairs. Recent advancement on engineering technology enables more intuitive, easy-to-use rehabilitation systems. A human-machine interface that uses non-invasive, electrophysiological signals can allow a systematic interaction between human and devices; for example, eye movement-based wheelchair control. However, the existing machine-interface platforms are obtrusive, uncomfortable, and often cause skin irritations as they require a metal electrode affixed to the skin with a gel and acrylic pad. Here, we introduce a bioelectronic system that makes dry, conformal contact to the skin. The mechanically comfortable sensor records high-fidelity electrooculograms, comparable to the conventional gel electrode. Quantitative signal analysis and infrared thermographs show the advantages of the soft biosensor for an ergonomic human-machine interface. A classification algorithm with an optimized set of features shows the accuracy of 94% with five eye movements. A Bluetooth-enabled system incorporating the soft bioelectronics demonstrates a precise, hands-free control of a robotic wheelchair via electrooculograms.