Oedipus is a tragic hero. He is, perhaps, the quintessential tragic hero, fulfilling Aristotle's definition exactly.
For Aristotle, a tragic hero possesses certain qualities. The hero is a person of value, demonstrating true quality and virtue. Though the hero can be flawed, he or she cannot be fundamentally weak or be a person characterized by vice.
Also, to be tragic, the hero must experience a fall, or tragedy, which comes about through no fault of his own. Often, the character's downfall will be the result of one of the character's strengths that is turned against him. This is commonly called the character's tragic or fatal flaw (hamartia).
Oedipus clearly meets these criteria. A strong and noble leader and a man of integrity, Oedipus demonstrates many fine qualities. Though he is quick to anger, he is not cruel at heart. He is open and bold and willing to sacrifice himself.
He is a tragic hero because he has virtue and meets a tragic fate through no fault of his own. He brings on his tragedy through his own sense of honesty and strength as he insists that he be told the truth about his past.