Although there is evidence that a person named Odysseus did in fact live in the time period Homer describes, little is known of his death. According to a lost epic poem called the Telegony, he died at the hands of the son he had with the goddess Circe. Tireasis, in the Odyssey, claims that he will die while sailing out on another adventure. The story of Dante's Inferno also suggests that his happened.
In real life, there is no documentation about his death, but it would appear that he did survive the Trojan War and did arrive back in his home of Ithaca. See the article I've attached for more information.
The Odysseus of Homer's Odyssey is a mythologized figure. Even if a real Odysseus existed in the time period Homer sings about in his epic poem, and even if the real Odysseus were the king of an island called Ithaca, there is very litttle evidence in the historic records to prove it.
The Odyssey ends with happiness--Odysseus is finally home in Ithaca after twenty years, reunited with his wife Penelope and his son Telemachus. However, earlier in the epic, during Odysseus's trip to the underworld, he met the blind prophet Tireasis, who told him that he would die a "death from the sea." What this means is unknown. It could refer to an adventure out on sea again, or it could refer to the death described in the Telegony, because his son with Circe comes from the sea in order to find him.