When King Elessar gave up his life Legolas followed at last the desire of his heart and sailed over Sea. We have heard that Legolas took Gimli Glóin’s son because of their great friendship, greater than any that has been between Elf and Dwarf. If this is true, then it is strange indeed: that a Dwarf should be willing to leave Middl-earth for any love, or that the Eldar should receive him, or that the Lords of the West [the Valar] should permit it. But it is said that Gimli went also out of desire to see again the beauty of Galadriel; and it may be that she, being mighty among the Eldar, obtained this grace for him.
Appendix A ‘One of the last notes in the Red Book’, The Return of the King (via forlornoccult)