We present \emph{DreamHuman}, a method to generate realistic animatable 3D human avatar models entirely from textual descriptions. Recent text-to-3D methods have made considerable strides in generation, but are still lacking in important aspects. Control and often spatial resolution remain limited, existing methods produce fixed rather than 3D human models that can be placed in different poses (i.e. re-posable or animatable), and anthropometric consistency for complex structures like people remains a challenge. \emph{DreamHuman} connects large text-to-image synthesis models, neural radiance fields, and statistical human body models in a novel optimization framework. This makes it possible to generate dynamic 3D human avatars with high-quality textures and learnt per-instance rigid and non rigid geometric deformations. We demonstrate that our method is capable to generate a wide variety of animatable, realistic 3D human models from text. These have diverse appearance, clothing, skin tones and body shapes, and outperform both generic text-to-3D approaches and previous text-based 3D avatar generators in visual fidelity.