The appointment follows the opening of a £42 million teaching building on the university’s Easter Bush Campus.
Professor Elaine Watson, who previously held the post, will become the university’s first Dean of International Veterinary Education and Business Development.
Professor John Savill, head of the university’s College of Medicine and Veterinary Medicine, said: “Professor Watson has made an outstanding contribution and the new teaching building stands as a testament to her vision and drive.
“Professor Argyle will bring a further wealth of experience as the new head of the school.
“This is an exciting time for veterinary education, with opportunities arising from investment at the Easter Bush campus.”