We report on the observation of D0–D0 bar oscillations by measuring the time-dependent ratio of decay rates for the rare decay D0 → K+ π− to the Cabibbo-favored decay D0 → K− π+ at the Collider Detector at Fermilab (CDF). Using 9.6 fb−1 of integrated luminosity recorded in the full CDF Run II, the signals of 7.6 × 106 D0 → K− π+ and 33 × 103 D0 → K+ π− decays are reconstructed in D∗ -tagged events, with proper decay times between 0.75 and 10 mean D0 lifetimes. Assuming CP conservation, we measure the mixing parameters x′2 = (0.08 ± 0.18) × 10−3 , y ′ = (4.3 ± 4.3) × 10−3 and the ratio of doubly-Cabibbo suppressed to Cabibbo-favored decay rates RD = (3.51 ± 0.35) × 10−3 . Our result excludes the no-mixing hypothesis with a probability equivalent to 6.1 standard deviations, confirming the recent LHCb observation and contributing important statistical precision to the mixing parameters.