The earthquake swarm accompanying the January 2022 Hunga Tonga‐Hunga Ha'apai (HTHH) volcanic eruption includes a large number of posteruptive moderate‐magnitude seismic events and presents a unique opportunity to use remote monitoring methods to characterize and compare seismic activity with other historical caldera‐forming eruptions. We compute improved epicentroid locations, magnitudes, and regional moment tensors of seismic events from this earthquake swarm using regional to teleseismic surface‐wave cross correlation and waveform modeling. Precise relative locations of 91 seismic events derived from 59,047 intermediate‐period Rayleigh‐ and Love‐wave cross‐correlation measurements collapse into a small area surrounding the volcano and exhibit a southeastern time‐dependent migration. Regional moment tensors and observed waveforms indicate that these events have a similar mechanism and exhibit a strong positive compensated linear vector dipole component. Precise relative magnitudes agree with regional moment tensor moment magnitude (⁠M_w⁠) estimates while also showing that event sizes and frequency increase during the days after the eruption followed by a period of several weeks of less frequent seismicity of a similar size. The combined information from visual observation and early geologic models indicate that the observed seismicity may be the result of a complex series of events that occurred after the explosive eruption on 15 January, possibly involving rapid resupply of the magma chamber shortly after the eruption and additional faulting and instability in the following weeks. In addition, we identify and characterize an M_w 4.5 event five days before the paroxysmal explosion on 15 January, indicating that additional seismic events preceding the main eruption could have been identified with improved local monitoring. Our analysis of the HTHH eruption sequence demonstrates the value of potentially utilizing teleseismic surface‐wave cross correlation and waveform modeling methods to assist in the detailed analysis of remote volcanic eruption sequences.