We examine the orbital evolution of the Giant planets (Jupiter, Saturn, Uranus and Neptune) towards their currently observed configuration. The planets underwent large-scale orbital migration, during the early formation stages of our Solar system, as a result of their interaction with (i) the proto-planetary gas disc (first ~3-5 My), and (ii) the remnant disk of planetesimals, leftover planet-core formation. The second migration phase has been modeled successfully (the so-called Nice model, Tsiganis et al 2005, Gomes et al 2005), the results showing a remarkable agreement with observations. However, linking the two migration phases together and finding the appropriate initial conditions for the planetary system is a challenging issue. Here we present new results of extensive numerical simulations of the two migration phases. We show that the natural outcome of gas-driven migration is a multiply resonant planetary configuration, similar to the well-known Laplace resonance of the Gallilean satellites. Only a limited number of quadruple resonances are possible, some of which remain stable for very long times, after the dispersal of the gas disc. The planets then undergo planetesimal-driven migration, following a path very similar to that described by the Nice model. Migration stops when the disc of planetesimals is scattered away (~100-200 My). The final planetary orbits are very similar to their currently observed ones, in terms of all three orbital parameters (semi-major axes, eccentricities, and mutual inclinations).