Untangling Tolkien - A Chronology and Commentary for The Lord of the Rings
The Tolkien Trust, run by the author's son Christopher, had earlier filed a lawsuit against Michael W Perry and his Inkling Books over the publication. US district judge Barbara Rothstein dismissed the case in January.
As no motion to reopen the case was filed in the 120 day period set by Judge Rothstein, the book can now be published.
"Everything is cleared up," Mr Perry said on Wednesday in Seattle. "The final settlement is signed."
A non-disclosure clause in the settlement prevented the details from being made public.
The book is entitled Untangling Tolkien: A Chronology and Commentary for The Lord of the Rings.
It was originally called The Lord of the Rings Diary: A Chronology of JRR Tolkien's Best-selling Epic.
In a joint statement the two parties said: "As Mr Perry has substantially changed the book, the estate has withdrawn its objection to publication of the book, but does not approve or in any way endorse the book as published."
The book is a timeline of the action and incidents in Tolkien's books, including The Lord of the Rings, the Hobbit and The Silmarillion. Tolkien did not write the books in chronological order.
Mr Perry's lawyer, Mel Simburg, said he had helped the author prepare the book "so that it more closely fit what he was trying to do, which was to create a chronology of fictional events".
One of Mr Perry's goals was to enable serious readers and fans of The Lord of the Rings to be able to tell what was happening at different places in the same time period, Mr Simburg said.
The case would appear to confirm that chronological references to a book's plot, complete with substantial analysis and commentary, are '"fair use", added Mr Simburg.
Mr Warren's Inkling Press makes the author only around $500 a month.
But two major publishers are said to have expressed an interest in his Tolkien chronology.