Water, the primary electrolyte in biology, attracts significant interest as an electrolyte-type dielectric material for transistors compatible with biological systems. Unfortunately, the fluidic nature and low ionic conductivity of water prevents its practical usage in such applications. Here, we describe the development of a solid state, megahertz-operating, water-based gate dielectric system for operating graphene transistors. The new electrolyte systems were prepared by dissolving metal-substituted DNA polyelectrolytes into water. The addition of these biocompatible polyelectrolytes induced hydrogelation to provide solid-state integrity to the system. They also enhanced the ionic conductivities of the electrolytes, which in turn led to the quick formation of an electric double layer at the graphene/electrolyte interface that is beneficial for modulating currents in graphene transistors at high frequencies. At the optimized conditions, the Na-DNA water-gel-gated flexible transistors and inverters were operated at frequencies above 1 MHz and 100 kHz, respectively.