Tuckwell is famous for his teaching. He has been Artist-in-Residence at Dartmouth College and Pomona College in the USA, and he was Professor of Horn at the Royal Academy of Music in London from 1963 until 1974. He taught at the Peabody Conservatory in Baltimore in the 1980s and 1990s. He was Professorial Fellow at the University of Melbourne and has for several years hosted the annual Barry Tuckwell Institute at Colorado Mesa University in Grand Junction, Colorado.