Narrow bandwidth is a fundamental issue plaguing practical applications of metamaterial absorbers. In this Letter, we show that by deliberately controlling the dispersion and dissipation of a metamaterial, an ultrawideband perfect metamaterial absorber with complex-valued constitutive parameters strictly satisfying the modified model of a perfectly matched layer, can be achieved. The nearly perfect power absorption, better than 99%, was experimentally observed in an unprecedented bandwidth of 39%, approaching the theoretical Rozanov limit. We expect a wide range of applications to emerge from this general concept.