Lawrence died Tuesday at his home in Mount Laurel, the university said. A cause of death was not disclosed.
Lawrence oversaw the university's first formal strategic plan, Rutgers' evolution into a more diverse institution and the remaking of the school's technology infrastructure.
Lawrence was born Aug. 25, 1937, and grew up in Woonsocket, R.I., before attending St. Louis University, where he earned his bachelor's degree.
He became a scholar of French literature and came to Rutgers as president in 1990 after spending three decades at Tulane University, where he earned his doctorate before becoming a professor and administrator. At Tulane, he was provost and dean of the graduate school.
At Rutgers, Lawrence reorganized the school's fundraising operations, bringing in more money, and oversaw a building boom across its campuses in New Brunswick and Piscataway, Newark and Camden.
Over the last seven years of his leadership, Rutgers added more than 50 new academic programs.
Lawrence remained a faculty member until he retired last year.
Lawrence is survived by his wife, Mary Kay, son Christopher Lawrence and daughters Naomi Lawrence and Jennifer Lawrence; 13 grandchildren and three sisters. A third daughter, Elizabeth Lawrence, had died.