Prof. Drexel studied medicine at the University of Innsbruck and graduated with exceptional honours, sub auspiciis praesidentis rei publicae. He did his specialist training at the University Clinic for Internal Medicine in Innsbruck (Director Prof. Dr. H. Bransteiner) followed by additional specialist trainings in cardiology, endocrinology, metabolic disease, and angiology. In 1984, he was awarded Venia Legendi (university teaching credentials making him Univ. Doz. for internal medicine) at the University Innsbruck, and 10 years later he became titular professor (tit. A.o. Univ. Prof.). From 1990 to 1993, he lectured at the University Hospital of Zurich, Department of Cardiology (Director Prof. Dr. F.W. Ammann) of the Medical Clinic (Director Univ.-Prof. Dr. F. Follath). 1992, 1994, 1996, and 2002 he visited the US for a research stay at the St. Elisabeth Medical Centre at Tufts University in Boston, MA, USA.

From 1994 to 2017, Prof. Drexel was Head of the Department for Internal Medicine at the State Hospital Feldkirch (LKHF). In 1994, he founded the Vorarlberg Institute for Vascular Investigation and Treatment (VIVIT), headquartered at the LKHF, and has been its CEO since inception. On 1st December 2020, Prof. Drexel became Head of the Department for Internal Medicine at the State Hospital Bregenz (LKHB).
A large number of publications in the world’s leading medical journals (New England Journal of Medicine, The Lancet, Circulation, Diabetes Care, Diabetologia, Atherosclerosis, American Heart Journal, American Journal of Cardiology, Pain, etc.) and extensive reviewer functions for the journals Diabetes Care, Diabetologia, European Heart Journal, etc. are testimony of his intensive publishing activities and his scientific excellence.

Moreover, Prof. Drexel is a member of national and international advisory boards. His medical focus area is internal medicine, his scientific focus areas are cardiovascular disease, diabetes, metabolism, cholesterol and pain research. He fulfils his teaching assignment for internal medicine at the LKHF, which is an academic teaching hospital of the Medical University of Innsbruck, by regularly giving lectures about internal medicine and pharmacology. From 2004 to 2006 he was Medical Director of the LKHF and from 2012 to 2013 he was President of the Austrian Diabetes Association (ÖDG).
From 2005 to 2020, Prof. Drexel was Director of Studies for the Doctorate Study of Medical Sciences (Dr. scient. Med.) at the Private University in the Principality of Liechtenstein.

Prof. Drexel is an active member of the scientific committee of the Federal State of Vorarlberg, and titles of honour such as the Fellowship of the European Society of Cardiology (FESC), the Fellowship of the American Heart Association (FAHA) and the Fellowship of the Royal College of Physicians Edinburgh (FRCP Ed.) are amongst his accolades.