Professor Connors attended Jesuit Regis High School in Manhattan studying classical languages. He graduated from Boston College with an A. B. in 1966. He received a second B. A. from Clare College, Cambridge University on a Marshall Scholarship in 1968. There the lectures of Nikolaus Pevsner convinced him to become an art historian. At Clare, too, he met a University of Paris student studying English literature, Françoise Moison. The two married in 1969. Connors returned to Boston, teaching at the Boston Latin [high] School (alma mater of Bernard Berenson). He entered Harvard University for graduate work. Connors taught as an instructor at Harvard, 1974-1975 before joining the University of Chicago as an instructor in 1975. His Ph.D was awarded in 1978 on the thesis topic of the Casa Filippini, Rome under the supervision of James Ackerman. In only three years he was promoted to associate (tenured) professor at the University of Chicago in 1978. The Frank Lloyd Wright architectural monument, Robie House, located on the grounds of the University, was the subject of his first book, somewhat surprisingly since Connors was a Baroque scholar.

In 1980 Connors returned to baroque Rome as a topic to publish Borromini and the Roman Oratory, receiving high acclaim. The same year, the new chair of the Columbia University department of art, Howard Hibbard, appointed Connors to associate professor of the faculty of art there. Connors advanced to full professor at Columbia in 1982. His Borromini book was awarded the Krautheimer Medal in 1984, a prize named for the architectural historian Richard Krautheimer. Connors accepted the director position of the American Academy in Rome in 1988, continuing to teach at Columbia until 2002. A large article, "Alliance and Enmity in Roman Baroque Urbanism," 1989, was his next book-length publication (it was issued as a book in the Italian translation of 2005). Connors edited and issued a guidebook based on a Columbia University manuscript, "Description de Rome moderne" generally ascribed to Lievin Cruyl (ca. 1640-1720) as Specchio di Roma barocca: una guida inedita del XVII secolo, assisted by his former student, Louise Rice.

In 1992 he was named Director of Villa I Tatti, the Renaissance research center housed in the former home of Berenson. He was succeded at the American Academy by Caroline Bruzelius (b. 1951). His paper, delivered at a joint conference of the British Museum and the Warburg Institute resulted in the 1992 essay, "Virtuoso Architecture in Cassiano's Rome.” Together with Jennifer Montagu, Connors wrote an historiographical introduction on Rudolf Wittkower to the new edition of Wittkower's Pelican History of Art on baroque Rome. In 2002 he assumed the directorship of Villa I Tatti, Harvard's Renaissance research center near Florence, Italy, succeeding Craig Hugh Smyth. As director he founded the Craig Hugh Smyth Fellowship, expanding I Tatti's library building and lecture space, and establishing the book series I Tatti Studies in Italian Renaissance History. His wife acted as Coordinator of Cultural Affairs at the center. He retired from I Tatti in 2010, succeeded by Lino Pertile, returning to Harvard College to teach.