Large-scale seafloor displacements can be at the origin of intense and destructive tsunami waves, thus constituting a significant risk for coastal communities. Accordingly, the accurate estimation of tsunamigenic potential of an event in Near-Real-Time (NRT) is fundamental to mitigate the tragic outcomes. In this perspective, an accurate representation of the source epicentral location and a precise geographical distribution of the surface displacements are strongly required. Such characterization remains, however, challenging for conventional methods due to the heterogeneous station distribution along active seismic faults. As an alternative, the ionospheric observations can serve as a meaningful complement due to their sensitivity to seismological forcing. The analysis of earthquake-induced ionospheric fluctuations known as Co-Seismic Ionospheric Disturbances (CSID) can provide critical insights on the source processes allowing the improvement of the current early tsunami warning system. In this study, we present a framework designed to automatically detect and localize earthquakes from ionospheric Total Electron Content (TEC) observations. Through a deep learning model, we first estimate the detection probability of a CSID arrival, prior to inverting the source parameters using a Bayesian migration-stacking procedure. This strategy is privileged for its ability to account for the uncertainties associated with detection altitude, acoustic velocity model and prior distributions of seismic parameters. Based on a Monte Carlo Markov Chain (MCMC) sampling strategy, the current inversion model can provide the resulting posterior distributions of each parameter within few minutes, serving as a promising initial step for the development of an operational NRT warning system.