Anderson joined the
Royal Scottish Museum as an Assistant Keeper in 1970. In 1975, he moved to the chemistry department of the
Science Museum, London. He became an Assistant Keeper of Chemistry. One of his challenges in 1976 was to incorporate materials from the history of medicine collection of the
Wellcome Collection of the History of Medicine, which were acquired as a permanent loan. He organised a conference and edited "an excellent and detailed account" to celebrate the 250th Anniversary of the Faculty of Medicine of the University of Edinburgh,
The Early Years of the Edinburgh Medical School. This was followed by a catalogue in 1978:
The Playfair Collection and the Teaching of Chemistry at the University of Edinburgh 1713–1858. Anderson was also in charge of the renovation and expansion of the chemistry and industrial chemistry galleries in 1977. From 1981 he was a Member of
Annals of Science's Editorial Board. Anderson returned to the
Royal Scottish Museum as director from 1984 to 1985. When the Royal Scottish Museum amalgamated with National Museum of Antiquities in 1985, he became the director of the new
National Museums of Scotland in
Edinburgh, a position he retained until 1992. In 1992 Anderson joined the
British Museum in London, where he was director from 1992 to 2002. Anderson oversaw the £100 million millennium project redevelopment of the British Museum's
Queen Elizabeth II Great Court, designed by
Norman Foster and opened by the
Queen on 6 December 2000. Anderson was succeeded as director of the British Museum in 2002 by
Neil MacGregor. Anderson has been president of the Scientific Instrument Commission of the
International Union of History and Philosophy of Science (1982–1997), and of the
British Society for the History of Science (1988–1990). Anderson has held visiting academic posts at the
Institute for Advanced Study,
Princeton University and at the
Centre for Research in the Arts, Social Sciences, and Humanities (CRASSH) at the
University of Cambridge (2002–2003). He is an Emeritus Fellow of
Clare Hall, Cambridge. As of 28 July 2016, Anderson became interim president and CEO of the
Chemical Heritage Foundation (now the
Science History Institute), a history of science organization in
Philadelphia, Pennsylvania, USA. He succeeded German historian of science
Carsten Reinhardt. On 11 January 2017, Anderson was named the institution's ongoing president and CEO. He was succeeded by
David Allen Cole as of 20 May 2020. Anderson has published at least 14 monographs or catalogues and at least 50 papers. the history of
museums, and the work of
Joseph Black and
Joseph Priestley. ==Awards and honors==