Prior to his appointment at the University of Minnesota in 1997 he was on the faculty of McGill University in Montreal. He has held postdoctoral or visiting appointments at the University of Chicago, East Carolina University, the University of Otago in New Zealand, and the University of Natal Medical School (now the Nelson R. Mandela School of Medicine), the first medical school in South Africa for non-white students.

Elliott received a Guggenheim Fellowship and a National Endowment for the Humanities Public Scholar Award in 2018. He was the Cary and Ann Maguire Chair in Ethics and American History at the John W. Kluge Center at the United States Library of Congress in 2019. He is a Member of the Institute for Advanced Study in Princeton, New Jersey, where he led a faculty seminar on bioethics in 2003–2004, and an honorary faculty member of the University of Otago Bioethics Centre in New Zealand. He is a fellow of the Hastings Center, an independent bioethics research institution.
From the passage extract the career wards as a bulleted list with year and name.
* 2018, Guggenheim Fellowship
* 2018, National Endowment for the Humanities Public Scholar