The 26-year-old shot 33 of 40 in the final to replicate the third place secured by Ed Ling at the Rio Games five years ago.
The Chelmsford shooter had arrived in Japan as one of the favourites for gold as the world and European champion but could not match the Czech duo of Jiri Liptak and David Kostelecky.
Liptak won gold and Kostelecky claimed silver after a dramatic shoot-off for the Olympic title.
Coward-Holley had made a shaky start, making only seven of his opening 10 shots, but then responded with 14 in a row to get back on track.
That run ended just as early pace-setter Jorge Orozco Diaz began to falter, with the Mexican ultimately finishing fourth after missing three shots in a row during the elimination period.
With Kostelecky three shots clear at that point, Coward-Holley had been level pegging with Liptak but a miss in the 38th shot ended his hopes of progressing further.
Coward-Holley was a promising rugby player in his teenage years but twice suffered cracked vertebra and slipped discs.
After being advised to give up the game, he returned to his first love of shooting, a sport he had previously "done for fun" in his youth.
Coward-Holley became the first Brit to win a world title in an Olympic shotgun discipline with trap gold in Italy in 2019 and has now followed that up with a podium place in Tokyo.
Coward-Holley said of his bronze medal: "It's a little bit of a mix of emotions. I'm a little bit lost for words. It's my first Olympics so to come away with a medal, it's phenomenal."
Asked how he had handled his nerves in the final, he added: "Being my first Olympic final, the first little bit of the final is always that little bit of tension, that little bit of nerves. But I thought, 'you've got this far, you've just got to relax and trust yourself that you can do it'."