The Oscar-winning trilogy's soundtrack triumphed over "Schindler's List" and "Gladiator" in the Classic FM poll, reported BBC online.
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, said the music played a "huge part" in the identity of films.