Parameters of the transition from classical dynamics of spin waves to the formation of a coherent magnon Bose–Einstein condensate have been obtained experimentally for the first time. The studies are performed on an yttrium iron garnet film beyond the radio frequency excitation region; thus, the coherent state of magnons is an eigenstate rather than a state induced by an external radio frequency field. The critical magnon density at the formation of the Bose–Einstein condensate is in good agreement with a theoretically predicted value. The transition is obtained at room temperature, which is possible owing to a small mass of magnons and their high density.