Raised in Yakima, Washington, he took his undergraduate degree from Reed College and studied history at St. John's College, Oxford University on a Rhodes scholarship. Before joining B.U., Westling taught at Centre College in Kentucky, Reed College, the University of California, Irvine, and at the University of California, Los Angeles.
Westling joined the Boston University faculty in 1974. He was named provost in 1984. In this role he was controversial B.U. president John Silber's top aide and twice served as acting president; first in 1987 while Silber was on sabbatical and again in 1990 while Silber was running for Governor. In 1996, he was chosen to succeed Silber, who became Chancellor of the University after a 25-year tenure as president. Westling's tenure came to an end in July 2002, when he resigned the presidency to return to teaching and research as a Professor of History and Humanities. Silber stepped down as chancellor and reassumed the presidency on an interim basis until Aram Chobanian was appointed president ad interim in October 2003.
During Westling's career as President of BU he made controversial statements about students with learning disabilities. "President Westling referred to students with learning disabilities as "a plague," and an indication of "a silent genetic catastrophe," and he has made similar statements in letters to the New York Times, the Boston Globe, campus newspapers, and students' parents." 
- Russell, Jenna (July 10, 2002). "Westling Resigns As BU President, Silber Takes Reins". The Boston Globe.
- Dembner, Alice (November 8, 1994). "Some see first hints of a Silber exit in new BU task force on succession". The Boston Globe.
- Higgins, Richard (September 10, 1987). "Maitre is Named Dean at B.U. School". The Boston Globe.