Born in 1955 in New Orleans, Vitter has served in several senior higher education administration posts.

[3] From 1980 to 1992, Vitter was a faculty member in the Department of Computer Science at Brown University in Providence, Rhode Island.

From 2002 to 2008, Vitter was the Frederick Hovde Dean of the College of Science at Purdue University in West Lafayette, Indiana.

[3] Vitter spent sabbatical leaves at the Mathematical Sciences Research Institute in Berkeley, CA; INRIA in Rocquencourt, France; Ecole Normale Supérieure in Paris; Bell Laboratories in Murray Hill, New Jersey; Aarhus University in Aarhus, Denmark, and INRIA in Sophia Antipolis, France.

[6] The Daily Mississippian, the student newspaper, characterized his tenure as chancellor as a time of both significant campus construction and "cultural transition", including efforts to enhance diversity and inclusiveness.

[5] He retired in 2020 as Distinguished Professor Emeritus; he continues to work as a consultant and hold an adjunct professorship at Tulane University in New Orleans, Louisiana.