In The Lord of the Rings and the published Silmarillion that's correct. But in some of the later drafts Tolkien wrote he moved away from that towards a story where the world had always been a sphere (often called the "roundworld" versions), seemingly in an attempt to add more realism to the story.

The "flat world made round" was recast as a somewhat primitive Mannish myth (as a way to recon the earlier writings).