Numerical simulations of planetary accretion have succeeded in matching most of the physical and orbital properties of the terrestrial planets with one glaring exception: they categorically form Mars analogs that are roughly an order of magnitude too massive (Raymond et al. 2009). The initial conditions that best reproduce the mass of Mars require that the inner planetesimal disk had an outer edge at 1 Astronomical Unit (AU) (Hansen 2009). To date, no mechanism has been shown to create this edge and remain compatible with the current-day solar system, in particular the existence of the asteroid belt. Here we show that a substantial gas-driven radial migration of the giant planets is the needed mechanism. Hydrodynamical simulations show that the evolution of Jupiter and Saturn in a gas-disk generically leads to a two-stage, inward-then-outward, migration where the extent of each stage of migration depends on a priori unconstrained disk parameters (Masset & Snellgrove 2001, Morbidelli et al. 2007, Pierens & Nelson 2008). We demonstrate with numerical simulations that, if Jupiter migrated inwards to 1.5 AU before migrating out towards its current location, its gravitational influence would truncate the inner planetesimal disk at 1 AU. The resulting disk naturally reproduces all the terrestrial planets including Mars. During the giant planets' migration, the asteroid belt is emptied and later re-populated from two distinct parent populations. This provides the first dynamical explanation for the current dichotomy of physical properties of the main asteroid belt, with anhydrous asteroids (S-type) in the inner part and primitive asteroids (C-type) in the outer part (Gradie & Tedesco 1982). Our model links the origin of the inner solar system -- explaining the mass of Mars and the properties of the asteroid belt -- to a realistic evolution of the giant planets. Thus Mars and the asteroid belt provide the first evidence for an early solar system evolution characterized by substantial gas-driven orbital migration of the giant planets, similar to what is inferred for extrasolar planet systems (Armitage 2007).Read less <