He is recognized as changing the way wind instruments are taught. An entry in the New Grove Dictionary of Music and Musicians says that his ideas prompted "reconsideration of the wind medium, establishing a model for the twenty thousand wind ensembles subsequently established in American schools."

Fennell came to Eastman School of Music as a student, invited by the school's dean, composer and conductor Howard Hanson. Six years later he became a faculty member.

He was known for his striking appearance, and his unorthodox teaching methods. According to the Democrat and Chronicle, he once taught a conducting class underwater in order to illustrate a point about baton control.

There is a hall named after Fennell in Kofu, Japan, and an American Society of Composers, Authors, and Publishers prize named after him. He was inducted into the American Classical Hall of Fame in 2001.