Soft and stretchable materials play an important role in the emerging fields of soft robotics, wearables, and stretchable electronics. Hydrogels are compelling materials for this application space because they are soft, chemically tunable, biocompatible, and ionically conductive. As such, hydrogels have been used for skin mountable sensors, such as electrocardiogram (ECG) electrodes, and show promise in emerging devices as stretchable transparent electrodes. Ultimately, these types of devices interface the hydrogel with rigid metallic electrodes to connect with electronic circuitry. Here, we show it is possible to interface hydrogel with liquid metal (eutectic gallium indium, EGaIn) electrodes to create completely soft and deformable contacts. EGaIn is noted for its low viscosity, low toxicity, and negligible volatility. The alloy can be patterned into non-spherical 2D and 3D shapes due to the presence of an ultra-thin oxide skin that forms on its surface. Because it is a liquid, the metal is extremely soft. As a case study, we interfaced EgaIn with hydrogels and tested it as soft electrodes for ECG. These electrodes require low impedance at biomedically relevant frequencies (1-50 Hz). Potentiostatic electrochemical impedance spectroscopy measurements show that capacitive effects at the hydrogel-EGaIn interface dominate the impedance at these low frequencies, yet can be reduced by utilizing embedded acidic and basic hydrogels that remove the native oxide skin. Increasing the ionic strength of the hydrogel also helps lower the impedance of the metal-hydrogel electrodes. The resulting devices have signal-to-noise ratios that exceed commercial ECG electrodes. The softness of these hydrogels can be modified without compromising the electrical properties to create truly soft electrodes. In addition to creating low impedance electrodes, it is possible to manipulate the interface between liquid metals and gels to create completely soft memory devices and soft diodes, or to utilize the electrodes to actuate hydrogel. Combining liquid metal with hydrogels represents a potential strategy of creating soft electrodes and other electronic componentns for bioelectronic applications, e-skins, and next-generation soft robotics.