We report the observation of B0s-B0s oscillations from a time-dependent measurement of the B0s-B0s oscillation frequency Δms. Using a data sample of 1  fb−1 of pp collisions at s√=1.96  TeV collected with the CDF II detector at the Fermilab Tevatron, we find signals of 5600 fully reconstructed hadronic Bs decays, 3100 partially reconstructed hadronic Bs decays, and 61 500 partially reconstructed semileptonic Bs decays. We measure the probability as a function of proper decay time that the Bs decays with the same, or opposite, flavor as the flavor at production, and we find a signal for B0s-B0s oscillations. The probability that random fluctuations could produce a comparable signal is 8×10−8, which exceeds 5σ significance. We measure Δms=17.77±0.10(stat)±0.07(syst)  ps−1 and extract |Vtd/Vts|=0.2060±0.0007(Δms)+0.0081−0.0060(Δmd+theor).