Graphene, with its unique combination of physical and electronic properties, holds great promise for biosensor and bioelectronic applications. In this respect, the development of graphene solution-gated field-effect transistor (SGFET) arrays capable of operation in aqueous environments will establish the real potential of graphene in this rapidly emerging field. Here, we report on a facile route for the scalable fabrication of such graphene transistor arrays and provide a comprehensive characterization of their operation in aqueous electrolytes. An on-chip structure for Hall-effect measurements allows the direct determination of charge carrier concentrations and mobilities under electrolyte gate control. The effect of the solution-gate potential on the electronic properties of graphene is explained using a model that considers the microscopic structure of water at the graphene/electrolyte interface. The graphene SGFETs exhibit a high transconductance and correspondingly high sensitivity, together with an effective gate noise as low as tens of mu V. Our study demonstrates that graphene SGFETs, with their facile technology, high transconductance, and low noise promise to far outperform state-of-the-art Si-based devices for biosensor and bioelectronic applications.