Fully reconfigurable add-drop filters (ADFs) have important applications in optical communication and information processing. Here, we demonstrate a broadly tunable add-drop filter based on a double-disk cavity optomechanical system, side-coupled with a pair of tapered fiber waveguides. We investigate the dependence of the through (drop) efficiency on coupling rates between the cavity and two waveguides by varying cavity-waveguide distances. By optimizing the cavity-waveguide coupling rates, a drop efficiency of 89% and a transmission of 1.9% have been achieved. Furthermore, tuning of the ADF is realized by changing the air gap of the double disk using a fiber tip, which is controlled by a piezoelectric nanostage. Benefiting from the large optomechanical coupling coefficient and the mechanical compliance of the double-disk microcavity, a tuning range of 8 nm has been realized using a voltage of 7 V on the piezoelectric nanostage, which is more than one free spectral range of the cavity. As a result, both the through and drop signals can be resonant with any wavelength within the transparent window of the cavity material, which indicates that the ADF is fully reconfigurable.