We use published models of the early solar system evolution with a slow, long-range and grainy migration of Neptune to predict the orbital element distributions and the number of modern-day Centaurs. The model distributions are biased by the Outer Solar System Origins Survey (OSSOS) simulator and compared with the OSSOS Centaur detections. We find an excellent match to the observed orbital distribution, including the wide range of orbital inclinations which was the most troublesome characteristic to fit in previous models. A dynamical model, in which the original population of outer disk planetesimals was calibrated from Jupiter trojans, is used to predict that OSSOS should detect 11 ± 4 Centaurs with semimajor axes of a < 30 au, perihelion distances of q > 7.5 au, and diameter of D > 10 km (absolute magnitude H r < 13.7 for a 6% albedo). This is consistent with 15 actual OSSOS Centaur detections with H r < 13.7. The population of Centaurs is estimated to be 21,000 ± 8000 for D > 10 km. The inner scattered disk at 50 < a < 200 au should contain (2.0 ± 0.8) × 107 D > 10 km bodies and the Oort cloud should contain (5.0 ± 1.9) × 108 D > 10 km comets. Population estimates for different diameter cutoffs can be obtained from the size distribution of Jupiter trojans (N(>D) ∝ D -2.1 for 5 < D < 100 km). We discuss model predictions for the Large Synoptic Survey Telescope observations of Centaurs.