I've heard many times that, in his final years, Tokien rejected the idea of a flat Arda, and embraced a new story in which the world was always round and the Sun and Moon existed from the beginning. However, the only texts I've found with this new version are an old Ainulindalë (which was substituted by later ones that returned to the flat-earth) and some texts in HoME: Morgoth's Ring (Myths Transformed). But all of these texts look very incomplete and/or abandoned. While, on the other hand, the Annals of Aman and Grey Annals of the same years tell the old story of the Sun and Moon coming after the Trees. Am I missing then something important? Is there some other text that proves that the round earth was the "true" version?
There is one text that confirms this, and it's not one you'd expect.
Enter the Hobbit
As originally published, the description of the kindreds of the Elves (in Chapter 8, Flies and Spiders) included the following text:
In the Wide World the Wood-elves lingered in the twilight before the raising of the Sun and Moon...
In the Wide World the Wood-elves lingered in the twilight of our Sun and Moon...
If the only version you know is the revised version this seems innocuous, but in context, and taking the original version into account, the time in which the Wood-elves lingered is clearly that between the departure of the High-elves to Valinor and the return of the Noldor.
Evidently therefore, the 1966 revisions reflect the later concept where the world was round and the sun and moon had always existed from the beginning, and are - so far as I know - the only case where this concept achieved final form and was published during Tolkien's lifetime.
It's clear from a reading of HoME that Tolkien viewed published texts as having some extra authority: he wasn't above changing them (as Chapter 5 of the Hobbit shows) but was reluctant to do so, and in any event he'd never changed this particular text since it's 1966 revision, so it confirms that yes, this was the final concept, and yes, it was expressed in an actual published text during Tolkien's lifetime.
The Silmarillion and related texts were of course never fully revised to reflect this concept, and there are serious chronological problems with them - relating to the timing of the awakening of Men and their corruption by Melkor - whichever way you slice it.
Put briefly, Men cannot have awoken before or at the same time as Elves (otherwise Elves cannot be the Firstborn), but in the later concept that leaves a very narrow timeslice during which Melkor could have found and corrupted them - between VY 1050 and VY 1090 - because after that Melkor was a prisoner in Valinor. Tolkien did want to push back the awakening of Men for sure, but this seems a little too far to me.
In both concepts it's actually impossible for Melkor to have corrupted Men after his return, since he was by then trapped in his Dark Lord form: he would not have been able to appear among Men "in our own form visible, but greater and more beautiful" at all. An obvious solution would have been to have Sauron - who was never captured - as the one who corrupted Men (and a nice irony in that their original corrupter would have done it all over again in Numenor) but that seems to have never occurred to Tolkien.
That's just one examples of the difficulties that arise from the adjusted concepts: the old story was really just too deeply embedded in the mythology.
This answer is fine. However, there's still the fact that in the published Lord of the Rings (even after revision) Tom Bombadil speaks explicitly about the flat earth being turned round. And in questions of canon is generally assumed that LotR comes before The Hobbit. Other than that, the line doesn't say that the Wood-elves lingered under the Sun before the Noldor arrived. As far as we know, it could mean that they were lingering under the Sun when the Noldor came back (thus after the creation of the Sun in the original myth). Besides, it doesn't really say anything about the shape of the Earth.
It depends how you define "definitive". Tolkien was always changing his mind about how his stories should unfold. For instance, Galadrial's movements were revised a number of times.
Tolkien was moving towards a stance that it was wrong for his mythology to be so fantastically unrealistic in its physics. So he started rewriting the stories to make them set in a universe that always contained a round world. But it wasn't finished, and Christopher published the flat world version instead. This is an excerpt from Letter 325, one of the last Tolkien wrote.
but if any keen-eyed observer from that shore had watched one of these ships he might have seen that it never became hull-down but dwindled only by distance until it vanished in the twilight: it followed the straight road to the true West and not the bent road of the earth's surface...This general idea lies behind the events of The Lord of the Rings and the Silmarillion, but it is not put forward as geologically or astronomically 'true'; except that some special physical catastrophe is supposed to lie behind the legends and marked the first stage in the succession of Men to dominion of the world. But the legends are mainly of 'Mannish' origin blended with those of the Sindar (Gray-elves) and others who had never left Middle-earth.