Some of the largest earthquakes yet observed occur along the broad interface between two converging tectonic plates called the megathrust. The extent of the megathrust and its associated seismicity differs with each subduction zone, but typically crustal deformation related to the rupture extends both in submarine and terrestrial environments. On land, this coseismic deformation is common observed with stationary instruments such as Global Navigational Satellite Systems (GNSS) or through satellite imagery using Interferometric Synthetic Aperture Radar (InSAR). In submarine environments, directly viewing seafloor displacements is more challenging. While seafloor geodetic devices do exist, their sparsity prohibits their integration into most rupture models. In order to infer seafloor deformation and relate it to fault slip, a proxy needs to be used. The best option is to incorporate tsunami waveforms as measured by open-ocean pressure gauges. Since the tsunami is thought to be directly related to the rapid deformation of the seafloor, its relationship to fault slip can be examined and used in earthquake studies. This dissertation seeks to constrain the rupture size and magnitude of tsunamigenic earthquakes through the inclusion of data from both traditional geodetic instruments and recently deployed open-ocean tsunami gauges. By collecting and processing on-land geodetic data and offshore tsunami waveforms, data sensitive to a larger region of the megathrust can be incorporated into finite-fault inverse modeling than if using only a single dataset. First, the sensitivity of the subduction zone model space to geodetic and tsunami waveform data is assessed. This provides a picture of where we can and cannot resolve rupture models when data is limited. It also highlights the issues that can ensue if poorly constrained models are used to study earthquakes. Second, I conduct an event-based joint inversion incorporating both geodetic and tsunami data for the 2015 Illapel earthquake. This includes merging codes for tsunami propagation, fault deformation, and linear inversions. The result of the joint inversion is a model space that is not only resolved near the coastline where geodetic data exists, but also near the trench where tsunami data is significantly more sensitive. The third component of this dissertation is an analysis of the feasibility of open-ocean data for rapid source inversions. This builds on current tsunami warning center methodologies but with a focus on the time constricted scenarios of a near-field warning from a local tsunami source. Here I analyze four different regions for their tsunamigenic potential as well as their potential to have instrumentation that will provide enough lead time during a local event to record data that is meaningful for disaster management and hazard warnings. The combination of these different aspects of tsunami-geodetic joint inversions illustrates both the improved model resolution and understanding of what was once a poorly constrained problem.