He continued to work with Scott as an SRC postdoctoral Research Fellow and Junior Research Fellow of Wolfson College, in Oxford, until 1976, when he moved to the USA, first as a Visiting Assistant Professor of Mathematics at Clark University in Worcester, Massachusetts, then, from 1977 to 1982, as JF Ritt Assistant Professor of Mathematics at Columbia University in New York.
In 1983 he moved, with a Science and Engineering Research Council Fellowship, to the Department of Electronic and Electrical Engineering at Brunel University. He was appointed to a Readership, and then to the Chair of Formal Systems, at Brunel in 1986.
Fourman was co-founder and Technical Director of Abstract Hardware Limited (AHL), a company formed in 1986. He was central in the development of the LAMBDA system (Logic And Mathematics Behind Design Automation) to aid hardware design, a tool implemented in the SML programming language and marketed by AHL. He left the company in 1997.
In 1988 he joined the Laboratory for Foundations of Computer Science at the University of Edinburgh, and was appointed to the Chair of Computer Systems in the Department of Computer Science.
In 1998 he was founding Head of the Division of Informatics, which became the current School of Informatics, incorporating the former Department of Artificial Intelligence, the Artificial Intelligence Applications Institute, the Centre for Cognitive Science, the Human Communication Research Centre, and the Department of Computer Science.
He has again been Head of the School of Informatics since August 2002.
He has held visiting positions at universities in Paris (1975), Utrecht (1977, 1980), Cambridge (1979–80), Sydney (1982), Montreal (1983), and Perth (1994).