The Tale of Aragorn and Arwen was written by Faramir and Éowyn's grandson, Barahir, after the death of Aragorn.
Gilraen warned her son against falling in love with an Elf-maiden of such a high status as Arwen, daughter of Lord Elrond, was. For a time, Aragorn left Imladris to aid in the fight against Sauron, and at the age of 49, went to stay in Lórien, where Arwen, unbeknown to him at the time, was also staying.
"And thus it was that Arwen first beheld him again after their long parting; and as he came walking towards her under the trees of Caras Galadhon laden with flowers of gold, her choice was made and her doom appointed."
On Cerin Amroth they plighted their troth, and Arwen forsook her immortality; following the War of the Ring, they were married and spent six-score years together. Aragorn found himself growing weary of life, and being one of the Dúnedain, blessed with long life, decided to return the gift he had been given.
After Aragorn's passing, Arwen bid farewell to her daughters, and to her son Eldarion, and went to Lórien, where she dwelled alone until winter arrived. She laid herself down upon Cerin Amroth sometime before Spring came, and there she remained until the end of her days.