Albert Barnes Commentary Ezra 1:2

"Thus saith Cyrus king of Persia, All the kingdoms of the earth hath Jehovah, the God of heaven, given me; and he hath charged me to build him a house in Jerusalem, which is in Judah." — Ezra 1:2 (ASV)

The Lord God of heaven — Or, “Yahweh, the God of heaven.” In the original Persian, the document probably read: “Ormazd, the God of heaven.” The Hebrew transcript took “Yahweh” as the equivalent of “Ormazd.” The Persian notion of a single Supreme Being—Ahura-Mazda, “the much-knowing, or much-bestowing Spirit”—did, in fact, closely approach the Jewish conception of Yahweh.

Hath given me all the kingdoms ... — There is a similar formula at the beginning of the great majority of Persian inscriptions.

He hath charged me to build him an house — It is a reasonable conjecture that, on the capture of Babylon, Cyrus was brought into contact with Daniel, who drew his attention to the prophecy of Isaiah (Isaiah 44:28); and that Cyrus accepted this prophecy as a “charge” to rebuild the temple.