•The inner Solar System’s water – the C-type asteroids and Earth’s water – are simple byproducts of giant planet growth.•The giant planets’ growth scatters nearby planetesimals and injects a significant fraction into the inner Solar System.•Scattered planetesimals are captured into the outer main belt and can explain the C-type asteroids.•Many water-rich planetesimals were scattered onto high-eccentricity orbits that crossed the growing terrestrial planets'.•Planetesimal scattering and implantation is robust to the planets' migration and occurs whenever a giant planet forms. There is a long-standing debate regarding the origin of the terrestrial planets’ water as well as the hydrated C-type asteroids. Here we show that the inner Solar System’s water is a simple byproduct of the giant planets’ formation. Giant planet cores accrete gas slowly until the conditions are met for a rapid phase of runaway growth. As a gas giant’s mass rapidly increases, the orbits of nearby planetesimals are destabilized and gravitationally scattered in all directions. Under the action of aerodynamic gas drag, a fraction of scattered planetesimals are deposited onto stable orbits interior to Jupiter’s. This process is effective in populating the outer main belt with C-type asteroids that originated from a broad (5-20 AU-wide) region of the disk. As the disk starts to dissipate, scattered planetesimals reach sufficiently eccentric orbits to cross the terrestrial planet region and deliver water to the growing Earth. This mechanism does not depend strongly on the giant planets’ orbital migration history and is generic: whenever a giant planet forms it invariably pollutes its inner planetary system with water-rich bodies.