Bose-Einstein condensation in a gas of magnons pumped by an incoherent pumping source is experimentally studied at room temperature. We demonstrate that the condensation can be achieved in a gas of bosons under conditions of incoherent pumping. The critical transition point is shown to be almost independent of the frequency spectrum of the pumping source and is solely determined by the density of magnons. The electromagnetic power radiated by the magnon condensate is found to scale quadratically with the pumping power. The obtained results are in a good agreement with the theory of Bose-Einstein condensation of quasiequilibrium magnons.