Drechsler holds degrees from Bridgewater College, the University of Virginia, the University of Marburg, and the German Post-Graduate School of Public Administration Speyer. Between 1993 and 2006, he was Professor of Public Administration and Government at the University of Tartu. Before coming to Estonia, and during this time, he taught at Universities of Marburg, Giessen, and Frankfurt am Main, all Germany. He was Visiting Professor of Sociology in Lund, Sweden, in 1997, and of Governance at the University of Erfurt, Germany, in 2007. Drechsler also teaches at the European Business School in Oestrich-Winkel, Germany. He has served as Advisor to the President of Estonia, as Executive Secretary with the German Wissenschaftsrat during German reunification, and, as an APSA Congressional Fellow, a Senior Legislative Analyst in the United States Congress. He was the Vice Chairman of the executive board of Praxis, Estonia’s pre-eminent public policy think-tank, and a member of the Innovation Policy Council of the Estonian Ministry of Economics
In Public Administration, Drechsler emphasizes the non-technocratic, non-managerial, "state sciences" approach that focuses on effectiveness rather than efficiency. In economics and public policy, he is a strong protagonist of the role of the state in economic growth and of innovation and industrial policy. He serves or has served as an advisor, especially in the areas of public manangement reform and innovation policy as well as e-governance, for national governments and international organizations, such as the OECD, Council of Europe, SIGMA, World Bank, European Union (Lisbon Strategy), Inter-American Development Bank, and United Nations (UNDP); he has worked, in different capacities, on the national development plans of, e.g., Estonia, Mongolia, Kazakhstan, Peru, Brazil, and Norway. Philosophically, Drechsler is a classical Hermeneutician, as one of the last students of the late Hans-Georg Gadamer.
Drechsler received the 1997 Estonian National Science Award, Social Science category, the 2001 Alena Brunovskà Award for Teaching Excellence in Public Administration, the 2002 Outstanding Alumnus Award from Bridgewater College, where he also delivered the annual W. Harold Row Endowed Lecture, in 2004, the Maarjamaa Rist, Estonia's Order of Merit, and in 2005, the German one, the Bundesverdienstkreuz.