Brain mapping studies are demonstrating that personality is based on neurobiology and neuroanatomy. I posted an extensive list of these studies in the post The Neuroscience of Extraversion and Introversion.
Several studies demonstrate the connection between the five-factor model of personality and structures in the brain:
1. Personality is reflected in the brain’s intrinsic functional architecture. (Link)
2. Testing predictions from personality neuroscience. Brain structure and the big five. (Link)
3. White matter integrity and five-factor personality measures in healthy adults. (Link)
In addition, the thousands of brain mapping studies indexed on PubMed also describe the role of the brain in human behavior.