Globular clusters are considered to be likely breeding grounds for compact binary mergers. In this paper, we demonstrate how the gravitational-wave signals produced by compact object mergers can act as tracers of globular cluster formation and evolution. Globular cluster formation is a long-standing mystery in astrophysics, with multiple competing theories describing when and how globular clusters formed. The limited sensitivity of electromagnetic telescopes inhibits our ability to directly observe globular cluster formation. However, with future audio-band detectors sensitive out to redshifts of z approximate to 50 for GW150914-like signals, gravitational-wave astronomy will enable us to probe the Universe when the first globular clusters formed. We simulate a population of binary black hole mergers from theoretically motivated globular cluster formation models, and construct redshift measurements consistent with the predicted accuracy of third-generation detectors. We show that we can locate the peak time of a cluster formation epoch during reionization to within 0.05Gyr after 1yr of observations. The peak of a formation epoch that coincides with the Universal star formation rate can be measured to within 0.4-10.5Gyr after 1yr of observations, depending on the relative weighting of the model components.