Magnetometry is a powerful technique for the non-invasive study of biological
and physical systems. A key challenge lies in the simultaneous optimization of
magnetic field sensitivity and maximum field range. In interferometry-based
magnetometry, a quantum two-level system acquires a dynamic phase in response
to an applied magnetic field. However, due to the 2{\pi} periodicity of the
phase, increasing the coherent interrogation time to improve sensitivity
results in reduced field range. Here we introduce a route towards both large
magnetic field range and high sensitivity via measurements of the geometric
phase acquired by a quantum two-level system. We experimentally demonstrate
geometric-phase magnetometry using the optically addressable electronic spin
associated with the nitrogen vacancy (NV) color center in diamond. Our approach
enables unwrapping of the 2{\pi} phase ambiguity, decoupling of magnetic field
range from sensitivity, and enhancement of the field range by about 400 times.
We also find additional improvement in sensitivity in the nonadiabatic regime,
and study how geometric-phase decoherence depends on adiabaticity. Our results
show that the geometric phase can be a versatile tool for quantum sensing
applications.