Burke was born in Derry, Northern Ireland,. He was educated at Maidstone Grammar School and at Jesus College at the University of Oxford, where he gained an MA in Middle English.

Later, Burke moved to Italy, where he lectured at universities in Bologna and Urbino as well as at English schools in that country. While in Italy, he was engaged in the creation of an English–Italian dictionary and the publication of an art encyclopedia.

In 1966, after a period of broadcasting work, Burke moved to London to join the BBC's Science and Features Department, where he hosted and co-hosted a number of programmes. He was fascinated by the possibilities of television and the potential to educate and entertain by making programmes about science and technology. He also worked for a while as a teacher of English as a Foreign Language at the Regency Language School in Ramsgate.

Burke first made his name as a reporter on the BBC science series Tomorrow's World. He was BBC television's science anchor and chief reporter on the Project Apollo missions, including being the main presenter on the BBC's coverage of the first moon landings in 1969.

Burke co-produced (with Mick Jackson) his most important work: a highly acclaimed 10-part documentary series Connections (1978) that was first aired on the BBC and subsequently on PBS channels in the United States. The series traced paths of invention and discovery through their interrelationships in history, with each episode chronicling a particular path, usually in chronological order, and was a great success for Burke. It was followed by the 20-part Connections2 (1994) and then the 10-part Connections3 (1997) series. Later, it was shown in more than 50 countries and appeared in about 350 university and college curricula. Additionally, the book that followed the series was also a best seller on both sides of the Atlantic.

In 1985, Burke produced a 10-part series The Day The Universe Changed (revised in 1995). This series focuses more on the philosophical aspects of scientific change on Western culture. Burke has also been a regular contributor for Scientific American and Time magazines and served as a consultant to the SETI project. He has received the Royal Television Society's silver and gold medals. In 1998 he was made an honorary fellow of the Society for Technical Communication.

In contrast with the end of Connections, in which Burke worried that computing and communications would increasingly be in the hands of an expert elite, in the closing scenes of The Day the Universe Changed he instead suggested that a forthcoming revolution in communication and computer technology would allow people all over the world to exchange ideas and opinions instantaneously. Subsequent events, such as the rise of popular access to the Internet, suggest he had been correct. His views of the connected nature of history have also been substantiated by recent research in chaos/complexity/network theory. See for example complex systems and six degrees of separation.

James Burke is the leading figure of the KnowledgeWeb Project. This is the digital incarnation of his books and television programmes, which allows the user to fly through history and create their own connective paths. According to the site, it will eventually have immersive, inhabited virtual reality recreations of historical people and places.

Television series and major single documentaries made by James Burke:

• The Burke Special (1972—1976)
• The End of the Beginning (1972), marking the end of Project Apollo
• Connections (1978)
• The Men who Walked on the Moon (1979), 10th anniversary of Apollo 11
• The Other Side of the Moon (1979), a more critical look at Apollo
• The Real Thing, on various aspects of perception (1980)
• The Neuron Suite on the human brain (1982)
• MacGillivray Freeman's Speed (1984), Narrator
• The Day the Universe Changed (1985, revised in 1995)
• After the Warming (1989), on the greenhouse effect
• Masters of Illusion (1993), on Renaissance painting
• Connections 2 (1994) (sometimes written Connections²)
• Connections 3 (1997) (or Connections³)
• Stump the Scientist, in which an audience of children were invited to put questions to a resident panel of scientists in the hope of "stumping" them
• ReConnections

The BBC topical comedy series 'Not The Nine O'Clock News' included a sketch in which Griff Rhys-Jones, imitating Burke, delivered a passage of elaborately mischievous prose somewhat in his manner, ending with the following: "So there we have it. It's all really very simple. And if it isn't, I make it up. So until then, goodbye.(Leaves the scene but suddenly appears again) Hello again. Ha! That fooled you, didn't it. Or, did it?"