We investigate the existence and propagation properties of linearly chirped self-similar solitons in an inhomogeneous tapered centrosymmetric nonlinear waveguide doped with resonant impurities under diffraction and nonlinearity management. The exact self-similar bright and dark soliton solutions are presented by employing an improved homogeneous balance principle and an F-expansion method. It is found that these chirped self-similar beams possess a strictly linear chirp that leads to efficient compression or amplification. The dynamical behaviors of these self-similar structures in a periodic distributed amplification waveguide system and an exponential diffraction decreasing waveguide are respectively studied for different choices of tapered index profile. The results show that the soliton shape and propagation behavior can be effectively controlled by selecting the diffraction, quintic nonlinearity, tapering, and gain or loss.