The present Letter shows that the formation of ozone in ternary collisions O+O_{2}+M-the primary mechanism of ozone formation in the stratosphere-at temperatures below 200 K (for M=Ar) proceeds through a formation of a temporary complex MO_{2}, while at temperatures above ∼700 K, the reaction proceeds mainly through a formation of long-lived vibrational resonances of O_{3}^{*}. At intermediate temperatures 200-700 K, the process cannot be viewed as a two-step mechanism, often used to simplify and approximate collisions of three atoms or molecules. The developed theoretical approach is applied to the reaction O+O_{2}+Ar because of extensive experimental data available. The rate coefficients for the formation of O_{3} in ternary collisions O+O_{2}+Ar without using two-step approximations were computed for the first time as a function of collision energy. Thermally averaged coefficients were derived for temperatures 5-900 K. It is found that the majority of O_{3} molecules formed initially are weakly bound. Accounting for the process of vibrational quenching of the nascent population, a good agreement with available experimental data for temperatures 100-900 K is obtained.