Juris Steprāns was born in Montreal in 1953 to parents who fled the Soviet occupation of Latvia. He finished his undergraduate education at the University of Waterloo and earned a doctorate from the University of Toronto in 1982. His thesis established that the truth or falsehood of various statements in mathematics could not be determined from the usual assumptions of set theory. Since it is known that all of mathematics can be constructed starting from set theory as a foundation, finding such independence results shows that the mathematical questions under consideration are not answerable without appealing to axioms beyond the usual framework. His work since then has focused on applying set theoretic methods to show that analysis, algebra, topology and other areas of mathematics are not immune from this independence phenomenon.

He has been a member of the Department of Mathematics and Statistics at York University since 1982. He is the author of some eighty research articles in various branches of mathematics, has presented invited lectures throughout North America, Europe and Asia and has supervised several PhD students and postdoctoral fellows. He has held visiting appointments at the University of Wisconsin, University of Warsaw and the University of Latvia and is a regular visitor to Rutgers University.

He has been elected to the Board of Directors of the Canadian Mathematical Society and chaired its Publications Committee. Juris Steprāns has also served on the Natural Sciences and Engineering Research Council of Canada and chaired one of its Grant Selection Committees. He has also served in a similar capacity for the National Science Foundation of the United States. From 2006 to 2010 he was the Deputy Director of the Fields Institute for the Mathematical Sciences and was the Acting Director for part of this term. He was elected a fellow of the Fields Institute in 2004. Juris Steprāns is also an editor of the Central European Journal of Mathematics.

He has been an elected member of the Board of Directors of the Latvian National Federation in Canada for many years and has also served on its Executive. He is currently a member of the Board of Directors of the Latvian Credit Union.