Yes, at the end of Return of the King (book) there's a whole section on what happened to the rest of the Fellowship. I believe in the last event on the timeline of the group (or close to the last one) it says Gimli and Legolas left Middle-Earth together. The first dwarf and elf to leave for the Grey Havens together, I think =)
After the death of Aragorn, Legolas built a ship in Ithilien and left Middle Earth with Gimly the Dwarf, his best friend. They sailed down Anduin and so over Sea. All other elves had already left Middle Earth and Legolas really loved the Sea.
"I will leave, I will leave the woods that bore me;
For our days are ending and our years failing."
yeah....and this part was not shown in the movie. in the book, we are told that Legolas and Gimli traveled together and then they left the middle earth in the end :'(