We demonstrate a novel approach to the control of the collapse of optical beams in Kerr media. To this end, we consider a combination of two magnetooptical (MO) phenomena, the Cotton-Mouton and Faraday effects, in order to introduce a suitable and tunable interplay between the induced linear and circular birefringences. Our numerical analysis confirms that a properly applied external magnetic field may alter the dynamics of the beam propagation in magnetic self-focusing bulk Kerr media. For a chosen value of the optical power, the acceleration, the delay or even the arrest of the collapse can be achieved. We demonstrate experimentally the magnetically-induced acceleration of the collapse in a ferrimagnetic yttrium iron garnet crystal (YIG).