The new series will tell stories based on what happened prior to The Fellowship Of The Ring - the first part of JRR Tolkien's trilogy.
Amazon is planning several series of the show, plus a possible spin off.
Director Peter Jackson's film adaptation of the trilogy - which won a combined 17 Oscars - made nearly $6bn (£4.57bn) at the box office.
Sharon Tal Ygyando, head of scripted series for Amazon, said: "The Lord of the Rings is a cultural phenomenon that has captured the imagination of generations of fans through literature and the big screen."
She went on to say the streaming site was "thrilled" to be taking fans "on a new epic journey in Middle-earth".
Amazon has yet to reveal a release date or who might feature in the TV adaptation.
The film version - which was released over three years between 2001 and 2003 - had a star-studded cast including Elijah Wood, Sir Ian McKellan, Orlando Bloom and Liv Tyler.
Many fans of the books and films appeared sceptical about the news of a TV version.