His grandfather ran a billiards club in Swansea, New South Wales, and Charlton began playing cue sports when he was nine years old.

[3] At the age of eleven, he defeated fellow Australian Walter Lindrum in a wartime snooker exhibition match,[3] and he made his first century break when he was seventeen.

[6] In the final of the 1973 World Snooker Championship, played as the best-of-75-frames, Charlton led Ray Reardon 10–5 and 12–10, before the pair were on level terms at both 12–12 and 13–13.

[8] At the start of the eighth session, Reardon was affected by the bright lighting that had been installed for the purposes of television coverage, and he lost the first three frames.

[8] According to snooker historian Clive Everton, "Charlton's dogged consistency proved no match for Reardon's flair and wider range of shots.

According to the match report in Snooker Scene magazine, Charlton then "started to falter in a fashion all too familiar with his failures on the brink of other world titles", and he lost 4-5.

Charlton's final appearance at the Crucible came in 1992, where he was defeated 10–0 by defending champion John Parrott in the first round, the only recorded whitewash in the World Championship until 2019.

[13] Charlton was known for playing with a very straight cue action and rarely hitting the ball with any sidespin, when a less conservative approach might have paid dividends.

He released a 30-minute beginners' instructional video, Eddie Charlton's Snooker, Pool & Trick Shots, in PAL VHS format.