We theoretically studied the reversible adsorption of polymers onto selective mixed brushes. Mixed brushes are recently developed self-adoptive materials that reversibly change their morphology in response to altering external stimuli. The above changes in the morphology result in the reversible formation of different patterns on the outer surface of the brush. It is shown that thus achieved patterning of the adsorbing surface of the mixed brush can dramatically enhance the adsorption of polymers onto this brush, as compared to the adsorption onto the homogeneous brush surface. By making use of the developed self-consistent field theory we calculate the surface excesses of homo- and co-polymers adsorbed on the binary mixed brush for the two different morphologies (`ripple' and random). The interplay between the depletion effect caused by the loss of the polymer entropy in the interior of the brush and binding interactions is shown to lead to a rich adsorption-desorption behavior. The surface excess of the adsorbed polymers is calculated as a function of the relation between the radius of gyration of the adsorbed polymers and characteristic size of the surface pattern. Shorter (relative to the size of the pattern) polymers are shown to better adsorb onto the regular patterned brush surface, as compared to the random brush surface.