1959-1963 NY State Regents College Fellowship, Brooklyn College
1963 American Institute of Chemists Award for Undergraduate Studies
1965-1967 US Public Health Service Predoctoral Fellowship, University of Chicago
1968-1971 US Public Health Service Postdoctoral Fellowship, University of Edinburgh and University of Chicago
1994-1995 John Simon Guggenheim Memorial Foundation Fellowship. Nonlinear dynamics and sudden cardiac death.
1998 Quebec Science selects research from Leon Glass' group as one of the 10 “discoveries of the year” (February 1998 issue)
1998- Fellow, Royal Society of Canada
1999- Fellow, American Physical Society
2000-2003 The Maclean’s Guides to Canadian Universities has identified as a “Popular Professor” at McGill
2003 Jacques-Rousseau Prize for Interdisciplinary Research, ACFAS
2008 Fellow, Society of Industrial and Applied Mathematics 
2009 Fellow, American Association for the Advancement of Science
2012 Canadian Cancer Society selects work on the effects of Vitamin D on gene expression in which Leon Glass participated as one of the "Top 10 Canadian Cancer Society research''
2013 Arthur T. Winfree Prize, Society for Mathematical Biology
2014-15 Lady Davis Fellowship, Jerusalem University
2015 Distinguished Alumni Award, Brooklyn College
2016 Fellow, Society for Mathematical Biology
2018 CAIMS-SCMAI Research Prize (The Canadian Applied and Industrial Mathematics Society)
2020 The McGill University Medal for Exceptional Academic Achievement