We synthesize and systematically characterize a novel type of magnetically tunable metamaterial absorber (MA) by integrating ferrite as a substrate or superstrate into a conventional passive MA. The nearly perfect absorption and tunability of this device is studied both numerically and experimentally within X-band (8-12 GHz) in a rectangular waveguide setup. Our measurements clearly show that the resonant frequency of the MA can be shifted across a wide frequency band by continuous adjustment of a magnetic field acting on the ferrite. Moreover, the effects of substrate/superstrate's thickness on the MA's tunability are discussed. The insight gained from the generic analysis enabled us to design an optimized tunable MA with relative frequency tuning range as larger as 11.5% while keeping the absorptivity higher than 98.5%. Our results pave a path towards applications with tunable devices, such as selective thermal emitters, sensors, and bolometers.