The detection of magnetic fields with nanoscale resolution is a fundamental challenge for scanning probe magnetometry, biosensing, and magnetic storage. Current technologies based on giant magnetoresistance and tunneling magnetoresistance are limited at small sizes by thermal magnetic noise and spin-torque instability. These limitations do not affect Hall sensors consisting of high mobility semiconductors or metal thin films, but the loss of magnetic flux throughout the sensor's thickness greatly limits spatial resolution and sensitivity. Here we demonstrate graphene extraordinary magnetoresistance devices that combine the Hall effect and enhanced geometric magnetoresistance, yielding sensitivities rivaling that of state of the art sensors but do so with subnanometer sense layer thickness at the sensor surface. Back-gating provides the ability to control sensor characteristics, which can mitigate both inherent variations in material properties and fabrication-induced device-to-device variability that is unavoidable at the nanoscale.