Shrinking spintronic devices to the nanoscale ultimately requires localized control of individual atomic magnetic moments. At these length scales, the exchange interaction plays important roles, such as in the stabilization of spin-quantization axes, the production of spin frustration, and creation of magnetic ordering. Here, we demonstrate the precise control of the exchange bias experienced by a single atom on a surface, covering an energy range of 4 orders of magnitude. The exchange interaction is continuously tunable from milli-eV to micro-eV by adjusting the separation between a spin-1/2 atom on a surface and the magnetic tip of a scanning tunneling microscope. We seamlessly combine inelastic electron tunneling spectroscopy and electron spin resonance to map out the different energy scales. This control of exchange bias over a wide span of energies provides versatile control of spin states, with applications ranging from precise tuning of quantum state properties, to strong exchange bias for local spin doping. In addition, we show that a time-varying exchange interaction generates a localized ac magnetic field that resonantly drives the surface spin. The static and dynamic control of the exchange interaction at the atomic scale provides a new tool to tune the quantum states of coupled-spin systems.