Telamon was born to Aeacus, the king of the island of Aegina in the Saronic Gulf, and Endeis, the daughter of the centaur Chiron, the wise creature who was half man and half horse and who trained the greatest heroes of Greece, though some say his mother was Plutia, a daughter of the river god Asopus. His brother was Peleus, who would later marry the sea nymph Thetis and become the father of Achilles, the greatest warrior of the Trojan War. Telamon also had a half-brother named Phocus, the son of Aeacus and the Nereid Psamathe, a sea nymph of extraordinary beauty, who was so skilled at athletics that he outshone both Telamon and Peleus in the games. The jealousy of the legitimate brothers grew until, during a discus throw or a quarrel over a game, they killed Phocus, either accidentally or by design, and hid his body in a wood or threw it into the sea. When Aeacus discovered the murder, he banished both Telamon and Peleus from Aegina forever.

Telamon sailed to the island of Salamis, which lay off the coast of Attica near Athens, and there he found a kingdom in need of a king. The king of Salamis, Cychreus, had no male heir, and Telamon married his daughter, who was called Glauce in some tellings and Periboea in others, and inherited the throne. He ruled Salamis with justice and strength, and his fame as a warrior grew until he was counted among the greatest heroes of his generation. When Jason, the son of Aeson and rightful heir to the throne of Iolcus, assembled the Argonauts to sail for the Golden Fleece, Telamon was one of the first to join, bringing his own ship or sailing aboard the Argo, the vessel built from the sacred oak of Dodona and fitted with a speaking beam that warned the crew of danger.

The voyage of the Argo was only the beginning of Telamon's adventures. He also took part in the Calydonian Boar Hunt, the great expedition sent by King Oeneus of Calydon to kill a monstrous boar that had been sent by Artemis, the virgin goddess of the hunt, to ravage the king's lands because he had failed to honour her in his harvest sacrifices. Telamon stood among the hunters, which included Meleager, the prince of Calydon, Atalanta, the swift-footed huntress, and many other heroes, and he fought the beast with spear and courage. The boar was eventually killed by Meleager, but the hunt ended in tragedy when Meleager murdered his uncles in a quarrel over the hide, and Telamon returned to Salamis with the memory of a hunt that had brought glory to some and death to others.

The most famous campaign of Telamon's life was the sack of Troy, not the great war of Agamemnon and Achilles that would come a generation later, but an earlier assault led by Heracles, the hero forced to complete twelve impossible labours. King Laomedon of Troy, the father of Priam who would later rule the city during the Trojan War, had cheated Poseidon, the god of the sea, and Apollo, the god of music and prophecy, of their wages after they built the walls of his city. Heracles gathered an army to punish the king, and Telamon sailed with him as his closest companion. When the Greeks assaulted the walls of Troy, Telamon was the first to breach them, throwing himself into the city with a fury that even Heracles admired. Heracles had promised that the first man to enter the city would receive the fairest prize, and when Telamon leaped through the gap in the wall, Heracles feared that the glory would go to another. He drew his sword and rushed after Telamon, but Telamon, seeing the hero's face, understood the danger and quickly began to pile stones into a heap, declaring that he was building an altar to Heracles the Glorious Victor. Heracles, flattered, sheathed his sword, and the two men sacked the city together. Laomedon and all his sons were killed except for Priam, who was ransomed, and Hesione, the king's daughter, was given to Telamon as his prize. She bore him two sons: Ajax, who would grow to be the mightiest warrior in Greece after Achilles, and Teucer, who would become the finest archer in the Greek army.

Telamon lived to see his sons sail to Troy with the Greek fleet, a war that was in some ways the continuation of the campaign he had fought with Heracles. Ajax the Great, as he was called to distinguish him from the lesser Ajax of Locris, was a tower of strength at Troy, second only to Achilles in prowess, and when Achilles was killed by Paris, the Trojan prince whose abduction of Helen had caused the war, Ajax claimed the dead hero's armour as the rightful successor. But Odysseus, the cunning king of Ithaca, won the armour by trickery, and Ajax, driven mad by the shame, fell upon his own sword. Teucer survived the war but was banished by Telamon for failing to bring Ajax home alive, or in some versions for failing to avenge his brother's death, and the old king died in grief and anger, his heart broken by the loss of the son who had been his greatest pride. Telamon was buried on Salamis, and his tomb was honoured by the islanders for centuries as the resting place of a hero who had stood beside Heracles and sacked the city that would one day destroy his own line.