This 9 in. cylinder was discovered in 1879 by Hormuzd Rasssm during his excavations of the Temple of Marduk in Babylon (modern Iraq) is now on display in the British Museum. It consists of 36 lines of cuneiform script that describe the conquest of Babylon, and aftermath, by Cyrus the Persian in 539 B.C.
Cyrus describes the incompetence of Nabonidus and how the god Marduk helped him conquer the city of Babylon. In the aftermath, he describes how he returned images of gods to selected countries and cities. Many commentators believe that the first return of the Jews from exile in Babylon was part of this general reinstitution of traditional worship—although neither the Jews nor Judah are mentioned on the Cyrus Cylinder.
The biblical texts describing Cyrus' permission to return are found in Ezra 1:2–4; 6:2-3, and 2 Chronicles 36:23.
Ezra 1:2 “This is what Cyrus king of Persia says: “ ‘The LORD, the God of heaven, has given me all the kingdoms of the earth and he has appointed me to build a temple for him at Jerusalem in Judah. 3 Anyone of his people among you—may his God be with him, and let him go up to Jerusalem in Judah and build the temple of the LORD, the God of Israel, the God who is in Jerusalem. 4 And the people of any place where survivors may now be living are to provide him with silver and gold, with goods and livestock, and with freewill offerings for the temple of God in Jerusalem.’”
For a discussion of this text see Fant, Clyde E., and Mitchell G. Reddish. Lost Treasures of the Bible — Understanding the Bible Through Archaeological Artifacts in World Museums. Grand Rapids, MI: Eerdmans, 2008, pp. 367–70, and a long article in Wikipedia.