In this article, we show the capability of a global navigation satellite system (GNSS) precise orbit determination (POD) low Earth orbit (LEO) data to detect anomalous ionospheric disturbances in the spectral range of the signals associated with earthquakes and tsunamis, applied to two of these events in Papua New Guinea (PNG) and the Solomon Islands during 2016. This is achieved thanks to the new PIES approach (POD-GNSS LEO Detrended Ionospheric Electron Content Significant Deviations). The significance of such ionospheric signals above the swarm LEOs is confirmed with different types of independent data: in situ electron density measurements provided by the Langmuir Probe (LP) onboard swarm LEOs, DORIS, and ground-based GNSS colocated measurements, as it is described in this article. In this way, we conclude the possible detection of the tsunami-related ionospheric gravity wave in PNG 2016 event, consistent with the most-recent theory, which shows that a tsunami (which is localized in space and time) excites a spectrum of gravity waves, some of which have faster horizontal phase speeds than the tsunami. We believe that this work shows as well the feasibility of a future potential monitoring system of ionospheric disturbances, to be made possible by hundreds of CubeSats with POD GNSS receivers among other appropriate sensors, and supported for real-time or near real-time confirmation and characterization by thousands of worldwide existing ground GNSS receivers.