According to [Tolkien Gateway](http://tolkiengateway.net/wiki/An%C3%A1rion):

> Aid did arrive when Elendil, Isildur, and the Dúnedain of Arnor, in league with the Elven King Gil-Galad, formed the Last Alliance of Elves and Men and marched south. Anárion joined the host in the plain between Cirith Gorgor and the Dead Marshes and fought in the Battle of Dagorlad. The Allies entered Mordor and laid the Siege of Barad-dûr, but **Anárion was slain by a thrown rock in 3440.**

This is sourced to *History of Middle-Earth* volume 12, *The Peoples of Middle-Earth*, section "The Heirs of Elendil".