Anton was educated at The High School of Glasgow and the University of Glasgow, where he graduated M.A. (Hons) in Political Economy (1984) and took a Ph.D. in Economics (1989). He was a Lecturer and Senior Lecturer at the University of Glasgow from 1984 to 1992, and Daniel Jack Professor of Political Economy from 1992 until 2007. He was Dean of the Faculty of Social Sciences, 2000 to 2004, and Vice-Principal (Strategy, Budgeting and Advancement) from 2004 until 2007. After two years as Principal and Vice-Chancellor of Heriot Watt University, he returned to University of Glasgow to take up his present post in 2009.
Professor Muscatelli has been a consultant to the World Bank and the European Commission, and was a member of the Panel of Economic Advisers of the Secretary of State for Scotland from 1998 to 2000. Since 2007, he has been an adviser to the House of Commons Treasury Select Committee on monetary policy, and in 2008 he was appointed to chair an independent expert group for the Calman Commission on Devolution, set up by the Scottish Parliament and led by the Chancellor of the University of Glasgow, Sir Kenneth Calman.
He chaired the Research and Commercialisation Committee of Universities Scotland in 2007-08 and from 2008 to 2010 was Convener of Universities Scotland and Vice-President of Universities UK. He was appointed a Fellow of the Royal Society of Edinburgh in 2001, and of the CESifo Economics Research Institute in Munich in 1999 In 2009 he was appointed Knight Commander (Commendatore) of the Republic of Italy for services to Economics and Higher Education. In 2012 he was awarded an honorary doctorate (Ll.D) from McGill University, Montreal, Canada. In April 2012 he was appointed to the Board of the Scottish Funding Council (SFC) which provides funding and oversight of all of Scotland's Colleges and Universities. From 2014 he is Honorary President of the David Hume Institute, succeeding Lord Steel. He has held visiting appointments in many universities, including in 2014, Guest Professor of Nankai University, Tianjin, China.