We integrate geodetic, geological and seismological observations in Tierra del Fuego, into a consistent and quantitative analysis, to better understand the current crustal deformation associated to the Magallanes-Fagnano Fault, that is, the transform boundary between the South American and Scotia plates at the southern tip of Patagonia. To obtain reliable geodetic estimates of the thickness of the seismogenic layer, we model the current seismic cycle from the great 1949 M_w ≃ 7.7 earthquake to the present, including the lasting effects of postseismic relaxation. The model parameters are constrained by Global Navigation Satellite System velocities obtained by reprocessing 24 years of observations in the island with up-to-date models and satellite products. We combine the observed deformation rates with long-term geological estimates of the slip rate in this transform system during the Holocene. The modeling results point to a seismogenic layer thickness of 15 ± 3 km and to fault planes inclined 63° ± 4°, dipping to the South. Along the sections of the Magallanes-Fagnano Fault in the island these results are consistent with a seismic moment deficit rate, per unit of length, of 3.2 ± 0.8 × 10¹² N m a⁻¹ km⁻¹, and a cumulative seismic moment, to date, equivalent to an earthquake of magnitude M_w ≃ 7. The postseismic viscoelastic relaxation, probably related to viscous flow in the mantle, affects the entire region up to ∼200 km away from the Magallanes-Fagnano Fault, and more than 60 years after the earthquake.