The Regius Chair of Engineering is a royal professorship in engineering, established since 1868 in the University of Edinburgh, Scotland. The chair is attached to the University's College of Science and Engineering, based in the King's Buildings in Edinburgh. Appointment to the Regius Chair is by Royal Warrant from the British monarch, on the recommendation of Scotland's First Minister.

A Regius Professor is a university professor who has, or originally had, royal patronage or appointment. They are a unique feature of academia in the United Kingdom and Ireland. The first Regius Professorship was in the field of medicine, and founded by the Scottish King James IV at the University of Aberdeen in 1497. Regius chairs have since been instituted in various universities, in disciplines judged to be fundamental and for which there is a continuing and significant need. Each was established by an English, Scottish, or British monarch, and following proper advertisement and interview through the offices of the university and the national government, the current monarch still appoints the professor. This royal imprimatur, and the relative rarity of these professorships, means a Regius chair is prestigious and highly sought-after.