Julius Rocca’s (2003) view is that the Greek-Roman physician Galen (129AD-c.210AD) was key in shifting medicine from a cardiocentric (ie heart centric) model to a encephalocentric (ie brain centric) model.

Galen has various works that deal with the brain in terms that seem familiar to “modern medicine” (“Anatomical procedures” in particular has a detailed description of human anatomy which Rocca verifies as accurate).

Nutton (Medical History 48(2) 2004) credits Arabic sources as containing many of the same details as Galen’s work and therefore may suggest that Galen was building on the information of his teachers or rivals (Lycus of Macedon).

Galen’s focus on the brain was in terms of its “philosophical” and “theological” value. Nutton (2004) believes that Galen was “ahead” of his contemporaries and predecessors in believing that the brain was the home of the soul. He was also the first (Nutton says) to trace nerves back to the brain.

Galen was an incredibly influential on medical thought in Late Antiquity and well into the Latin Middle Ages. Rocca and Nutton both give Galen credit for introducing the idea of the brain as the “seat of consciousness and cognition” as you say.

Basically in extreme brief, Galen introduced the idea that the brain is the ‘control centre’ of the body by tracing nerves back to the brain.

(Rocca, Julius and Galen (2003) Galen on the brain: anatomical knowledge and physiological speculation in the second century AD. Leiden)