The Oscar-winning trilogy's soundtrack triumphed over Schindler's List and Gladiator in the Classic FM poll.
John Williams's compositions for Star Wars and John Barry's Out of Africa rounded out the top five.
Williams' music featured eight times in the top 30, including Jurassic Park, Saving Private Ryan, E.T. and Raiders Of The Lost Ark.
The top 100 movies were included in the hall of fame based on listener votes.
Elijah Wood, who played Frodo Baggins in The Lord Of The Rings trilogy, told Classic FM music played a "huge part" in the identity of films.
He added: "I think film scores are always extremely important with regard to the atmosphere and the emotional connection that you have to a film.
"Those pieces of music - you think about the Hobbiton theme - they're really iconic.
"They sort of transcend the films themselves, almost like John Williams' [scores]. The pieces from Star Wars are so iconic. We hear the music, we know the films and I think to a certain degree that's the case with Rings too, with Howard Shore's score."
There was a surge in the popularity of film music composed by James Horner, who was killed in a plane crash in June this year.
Four of his soundtracks - Braveheart, Titanic, Apollo 13 and Avatar - all climbed the chart.
Zimmer's score to Interstellar, starring Matthew McConaughey and Anne Hathaway, was the chart's highest new entry at number 43.
Music from The Lord of the Rings has been voted the best soundtrack of all time for the sixth year running.