They would have been used to the idea that King David was anointed by God to save these people from their enemies (See Psalms 2 and 110 for example). And David knew that he was God's servant designated to protect God's people.
Isaiah tells us that this Cyrus, king of a foreign people, is anointed by God to fulfill God's purpose. And, unlike David, Cyrus doesn't know God at the time of appointment.
This Persian leader will defeat Babylon thus releasing Israel from its exile.
God has saved these people once more. Saved them for their sake and for the sake of Cyrus and for the sake of all people who learn about God through Cyrus' victory.
Our blessings may come to us from what seems unlikely sources. People may do good things for us even if we don't consider them appropriately religious, v. 4. Our blessings are not to be hoarded, vs.3 and 6.
Lectio Divina: Isaiah 45:4-5