He was educated at Berklee College of Music in Boston and the Guildhall School of Music and Drama in London, and holds a Ph.D. from the University of Glamorgan. He also studied music, privately, with Alan Dawson, Peter Ind, Tony Oxley, James Blades, and David Arnold as well as movement with Bruno Tonioli and drama with Uta Hagen.

In the early 1980s he emerged as the first producer of the New Romantic movement, producing Spandau Ballet's first two gold albums and first six hit singles. He won a Music Week magazine sales award as a producer, and has created twenty four chart singles and fourteen hit albums.

Other productions included Adam Ant, King, New Edition, Melba Moore, Colonel Abrams, America, Kim Wilde, Five Star, Tony Banks of Genesis, and Fish of Marillion), Living in a Box, Princess, Virginia Astley, Errol Brown of Hot Chocolate, When In Rome, Shriekback, Shock and Barbie Wilde. He was also an ambient pioneer in producing the British group Praise. He produced, engineered and mixed albums by Rubicon and X-CNN under the pseudonym Caleb Kadesh and did several mixes using the pseudonym Cadillac Jack.

Burgess co-produced, co-wrote, programmed, sang and played drums for the European electronica group Landscape, whose album From The Tearooms Of Mars To The Hellholes Of Uranus yielded the international hits "Einstein A Go Go" and "Norman Bates". His studio-drumming career includes albums such as Adam Ant's Strip and The Buggles’ The Age of Plastic. As a Capitol Records solo artist he charted singles on the Billboard Hot Dance Club Play chart reaching No. 1 on the New York Dance Music Report chart. He also recorded with the British National Youth Jazz Orchestra and jazz musicians Neil Ardley, Ian Carr and Nucleus and played with Graham Collier OBE. He currently produces and plays drums for the blues band Electrofied and plays with jazz pianist Mickey Basil.

Burgess’s mixes and remixes include tracks for the movies 9½ Weeks, About Last Night and artists Thomas Dolby, Lou Reed, Youssou N'Dour, and Luba.

He defined the computer programmer's and sampler's role in modern music via his work in the 1970s, creating the first computer driven hit, "Einstein A Go-Go", with the Roland MC-8 Microcomposer and his first use of samples on commercial recordings with Fairlight CMI firsts such as Kate Bush's Never Forever album and Visage's single "Fade To Grey". He conceptualized and co-designed the first standalone electronic drum-set, the hexagonal shaped SDS5. He appeared three times on the BBC Television program Tomorrow's World demonstrating his prototype of this invention; use of the Roland MC-8 Microcomposer computer in pop music; and the world's first digital sampling machine the Fairlight CMI. He coined the name for the New Romantic movement of the early 1980s.< His New York productions of Colonel Abrams' which yielded the gold singles "Trapped" and "I'm Not Gonna Let" are widely considered to have been the precursors to house music.

With the avant-garde electronic group Accord he was featured on BBC Radio 3 programmes "Music In Our Time" and "Improvisation Workshop". He was selected to play in the British National Youth Jazz Orchestra, won the Greater London Arts Association’s Young Jazz Musicians award, the Vitavox Live Sound award and was chosen for the British Arts Council's Park Lane Group Purcell Room concert series. He is featured in The A to Z of Rock Drummers.

His book The Art of Music Production, which was originally entitled The Art of Record Production, is now in its third edition. He has written many articles for technical and music magazines, as well as articles and papers for the academic journal of The Association for the Study of the Art of Record Production (ASARP) He has lectured on the subject of record production and the music business in the United States and in the United Kingdom. He wrote and presented the BBC World Service radio series "Let There Be Drums". He taught drums at the Annapolis Music School in Maryland, and currently teaches classes on record production and the music business at The Omega Studios' School Of Applied Recording Arts And Sciences.

Burgess is the Director of Marketing and Sales for Smithsonian Folkways Recordings and Smithsonian Global Sound, Director of Resource Development for the Smithsonian Center for Folklife and Cultural Heritage and runs his own artist management company, Burgess Worldco in the Washington, D.C. area. He has been a Governor for the Washington, D.C. Chapter of the National Academy of Recording Arts and Sciences and is the co-chair for both the DC Chapter of the Producer and Engineer Wing, and the national Producer Compensation Committee.