First, we should note that Oedipus Tyrannus and Oedipus at Colonus were not parts of a trilogy, as they were not originally performed together, but rather two plays Sophocles wrote at different periods in his life, with Oedipus at Colonus being written and performed after both Oedipus Tyrannus and Antigone.
Second, Sophocles was actually a native of Colonus, a village in Attica outside Athens, and this play is meant to honor his home town, and probably a temple at which he was a priest, by showing that Athens was a city of peace, justice, and reconciliation, a theme that also appears in the Eumenides of Aeschylus.
In the earlier play, Oedipus is horrified when he discovers the nature of his acts, and reacts by stabbing himself in the eyes to blind himself and exiling himself from Thebes. The older Oedipus we see is wiser and calmer. Rather than feeling guilt, he defends his actions, saying that they were done in ignorance and that he never intended evil.
When Zeus gives the sign of a thunderstorm, Oedipus peacefully walks to his death, now viewing his curse and its resolution not as something horrifying but as a gift that he can give to Athens. As in the Eumenides, the earlier cycles of pollution and retribution have been transformed into opportunities for expiation and reconciliation.