Baugh was born in Port Antonio, Jamaica, the son of Edward Percival Baugh, Purchasing Agent and Ethel Maud Duhaney-Baugh. He began writing poetry at Titchfield High School. He won a scholarship to study English literature at the University College of the West Indies in Mona, Jamaica, and later did postgraduate studies at Queen's University in Ontario and the University of Manchester, where he earned a Ph.D. in 1964. He taught at the Cave Hill campus of the University of the West Indies from 1965 to 1967, then at the university's Mona campus from 1968 to 2001, eventually being appointed professor of English in 1978 and public orator in 1985. He has also held visiting appointments at the University of California, Dalhousie University, University of Hull, University of Wollongong, Flinders University, Macquarie University, University of Miami and Howard University.
His scholarly publications include West Indian Poetry 1900-1970: A Study in Cultural Decolonisation (1971); Critics on Caribbean Literature (1978); Derek Walcott: Memory as Vision (1978), the first book-length study of Walcott's work; and an annotated edition of Walcott’s Another Life (2004), with Colbert Nepaulsingh. Chancellor, I Present (1998) collects a number of the addresses Baugh delivered as UWI's public orator on the occasion of the presentation on honorary degrees.
Baugh's poems appeared in various magazines and anthologies years before the publication of his first collection, A Tale from the Rainforest (1988). This was followed by It Was the Singing (2000).
- It Was the Singing (2000)
- I Was a Teacher Too (1991)
- A Tale from the Rainforest (1988)
- Derek Walcott: Memory as Vision: "Another Life" (1978)
- Critics on Caribbean Literature (1978)
- West Indian Poetry 1900-1970: A Study in Cultural Decolonisation (1971)
- Carolyn Cooper, "6th Edward Baugh Distinguished lecture". Jamaica Woman Tongue, 27 November 2012.
- The Literary Encyclopedia.
- Yvonne Grinam-Nicholson, "Professor Edward Baugh - Living the years", The Jamaica Gleaner.
- "Edward Alston Cecil Baugh", The West Indian Encyclopedia.
- "Professor Edward Baugh", The University of the West Indies at Mona, Jamaica.
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- "Interview with Jamaican poet, Edward Baugh", Commonwealth Writers. 21 April 2012.
- "Part 3: Guest Speaker Professor Emeritus Edward Baugh, CD" on YouTube.