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The 1992 M-w 7.3 Landers and 1999 M-w 7.1 Hector Mine earthquakes struck the Eastern California Shear Zone (ECSZ) in the Mojave Desert, Southern California. Coseismic and postseismic deformation from these events affect efforts to use Global Positioning System (GPS) observations collected since these events to establish a secular surface velocity field, especially in the near field of the coseismic ruptures. We devise block motion models constrained by both historical pre-Landers triangulation and trilateration observations and post-Landers GPS measurements to recover the secular deformation field and differentiate the postseismic transients in the Mojave region. Postseismic transients are found to remain in the Southern California Earthquake Center Crustal Motion Map Version 4, Plate Boundary Observatory, and Scripps Orbit and Permanent Array Center GPS velocity solutions in the form of 2-3mm/yr excess right-lateral shear across the Landers and Hector Mine coseismic ruptures. The cumulative deformation rate across the Mojave ECSZ is 13.2-14.4mm/yr, at least twice the geologic rate since the late Pleistocene (6.21.9mm/yr). Postseismic GPS time series based on our secular velocity field reveal enduring late-stage transient motions in the near field of the coseismic ruptures that provide new constraints on the rheological structure of the lower crust and upper mantle.