Context. There are numerous extrasolar giant planets which orbit close to their central stars. These "hot- Jupiters" probably formed in the outer, cooler regions of their protoplanetary disks, and migrated inward to similar to 0.1 AU. Since these giant planets must have migrated through their inner systems at an early time, it is uncertain whether they could have formed or retained terrestrial planets. Aims. We present a series of calculations aimed at examining how an inner system of planetesimals/protoplanets, undergoing terrestrial planet formation, evolves under the influence of a giant planet undergoing inward type II migration through the region bounded between 5 - 0.1 AU. Methods. We have previously simulated the effect of gas giant planet migration on an inner system protoplanet/planetesimal disk using a N-body code which included gas drag and a prescribed migration rate. We update our calculations here with an improved model that incorporates a viscously evolving gas disk, annular gap and inner-cavity formation due to the gravitational field of the giant planet, and self-consistent evolution of the giant's orbit. Results. We find that greater than or similar to 60% of the solids disk survives by being scattered by the giant planet into external orbits. Planetesimals are scattered outward almost as efficiently as protoplanets, resulting in the regeneration of a solids disk where dynamical friction is strong and terrestrial planet formation is able to resume. A simulation that was extended for a few Myr after the migration of the giant planet halted at 0.1 AU, resulted in an apparently stable planet of similar to 2 m(circle plus). forming in the habitable zone. Migration - induced mixing of volatile-rich material from beyond the "snowline" into the inner disk regions means that terrestrial planets that form there are likely to be water-rich. Conclusions. We predict that hot-Jupiter systems are likely to harbor water- abundant terrestrial planets in their habitable zones. These planets may be detected by future planet search missions.