The power-controlled transformation of Gaussian beams in strongly nonlocal nonlinear media is investigated. Based on the relation between the solution for the free propagation and that for the strongly nonlocal nonlinear propagation, the field at the output plane is obtained, and then the analytical solution for the output Gaussian beam is obtained. With the increase of the input power, the waist is located alternatively at the left- and right-hand side of the output plane; and the waist width varies oscillatorily. Therefore, one can make a continuously steerable transformation on the Gaussian beam if appropriate input power range is chosen.