The reunion between Penelope and Odysseus finally takes place in the second to last book of the Odyssey, Book 23. The old nurse, Eurycleia, has found out the traveler's identity, and she tells Penelope. Penelope, who is cautious as well as wise, refuses to believe it immediately. Penelope is hopeful that it is Odysseus, but she must perform a test to make certain. She goes to see Odysseus in the hall, and he believes that she doesn't recognize him because of his dirty traveling clothes. He bathes and returns, and when the husband and wife speak Penelope suggests that he might like his old bed brought to him and arranged outside. He is shocked, for their marriage bed had been built around a live olive tree growing out of the ground in their bedroom. He says, distressed, that he hopes that no one has cut down that olive tree and destroyed their bed, and then Penelope knows for certain that this can be none other than Odysseus.
Source: Homer, The Odyssey. W.H.D. Rous, trans. Mentor Books: New York, 1950.