between 100 GeV and 20 TeV with the Very Energetic Radiation Imaging Telescope Array and Major Atmospheric Gamma Imaging Cherenkov telescope arrays. The binary orbit has a period of approximately 50 years, with the most recent periastron occurring on 2017 November 13. Our observations span from 18 months prior to periastron to one month after. A new point-like gamma-ray source is detected, coincident with the location of PSR J2032+4127/MT91 213. The gamma-ray light curve and spectrum are well characterized over the periastron passage. The flux is variable over at least an order of magnitude, peaking at periastron, thus providing a firm association of the TeV source with the pulsar/Be star system. Observations prior to periastron show a cutoff in the spectrum at an energy around 0.5 TeV. This result adds a new member to the small population of known TeV binaries, and it identifies only the second source of this class in which the nature and properties of the compact object are firmly established. We compare the gamma-ray results with the light curve measured with the X-ray Telescope on board the Neil Gehrels Swift Observatory and with the predictions of recent theoretical models of the system. We conclude that significant revision of the models is required to explain the details of the emission that we have observed, and we discuss the relationship between the binary system and the overlapping steady extended source, TeV J2032+4130.