The detectors of the laser interferometer gravitational-wave observatory (LIGO) are broadly limited by the quantum noise and rely on the injection of squeezed states of light to achieve their full sensitivity. Squeezing improvement is limited by mode mismatch between the elements of the squeezer and the interferometer. In the current LIGO detectors, there is no way to actively mitigate this mode mismatch. This paper presents a new deformable mirror for wavefront control that meets the active mode matching requirements of advanced LIGO. The active element is a piezo-electric transducer, which actuates on the radius of curvature of a 5 mm thick mirror via an axisymmetric flexure. The operating range of the deformable mirror is 120±8 mD in vacuum and an additional 200 mD adjustment range accessible out of vacuum. Combining the operating range and the adjustable static offset, it is possible to deform a flat mirror from -65 mD to -385 mD. The measured bandwidth of the actuator and driver electronics is 6.8 Hz. The scattering into higher-order modes is measured to be <0.2% over the nominal beam radius. These piezo-deformable mirrors meet the stringent noise and vacuum requirements of advanced LIGO and will be used for the next observing run (O4) to control the mode-matching between the squeezer and the interferometer.