This paper proposes BODYFITR, a fully automatic method to fit a human body model to static 3D scans with complex poses. Automatic and reliable 3D human body fitting is necessary for many applications related to healthcare, digital ergonomics, avatar creation and security, especially in industrial contexts for large-scale product design. Existing works either make prior assumptions on the pose, require manual annotation of the data or have difficulty handling complex poses. This work addresses these limitations by providing a novel automatic fitting pipeline with carefully integrated building blocks designed for a systematic and robust approach. It is validated on the 3DBodyTex dataset, with hundreds of high-quality 3D body scans, and shown to outperform prior works in static body pose and shape estimation, qualitatively and quantitatively. The method is also applied to the creation of realistic 3D avatars from the high-quality texture scans of 3DBodyTex, further demonstrating its capabilities.