Astronomical observations reveal that protoplanetary disks around young stars commonly have ring- and gap-like structures in their dust distributions. These features are associated with pressure bumps trapping dust particles at specific locations, which simulations show are ideal sites for planetesimal formation. Here we show that our Solar System may have formed from rings of planetesimals—created by pressure bumps—rather than a continuous disk. We model the gaseous disk phase assuming the existence of pressure bumps near the silicate sublimation line (at T ~ 1,400 K), water snowline (at T ~ 170 K) and CO snowline (at T ~ 30 K). Our simulations show that dust piles up at the bumps and forms up to three rings of planetesimals: a narrow ring near 1 au, a wide ring between ~3–4 au and ~10–20 au and a distant ring between ~20 au and ~45 au. We use a series of simulations to follow the evolution of the innermost ring and show how it can explain the orbital structure of the inner Solar System and provides a framework to explain the origins of isotopic signatures of Earth, Mars and different classes of meteorites. The central ring contains enough mass to explain the rapid growth of the giant planets’ cores. The outermost ring is consistent with dynamical models of Solar System evolution proposing that the early Solar System had a primordial planetesimal disk beyond the current orbit of Uranus.