This from Bible World History
Jeremiah 25:9-12 (NIV)
"I will summon all the peoples of the north and my servant Nebuchadnezzar king of Babylon," declares the Lord, "and I will bring them against this land and its inhabitants and against all the surrounding nations. I will completely destroy them and make them an object of horror and scorn, and an everlasting ruin. I will banish from them the sounds of joy and gladness, the voices of bride and bridegroom, the sound of millstones and the light of the lamp. This whole country will become a desolate wasteland, and these nations will serve the king of Babylon seventy years. "But when the seventy years are fulfilled, I will punish the king of Babylon and his nation, the land of the Babylonians, for their guilt," declares the Lord, "and will make it desolate forever."
Jeremiah 29:10 (NIV)
This is what the Lord says: "When seventy years are completed for Babylon, I will come to you and fulfil my gracious promise to bring you back to this place."
It seems clear from the context in these two segments that the seventy years applies to Babylon itself, not to the period of time that the people of Judah are to spend in Babylon. In chapter 25 it says that the nations would serve Babylon for 70 years. Again in chapter 29, Jeremiah makes the connection to Babylon by saying that 70 years are "for Babylon".
So the 70 years refers to the period of Babylonian Empire. When did this start and finish? As alluded to earlier, Babylon was conquered by Cyrus II of Persia in 539 BC. So this is the finish. When was the start? For our purposes, the start would have to be when the other "nations will serve the king of Babylon" (see excerpt from Jeremiah 25 above). The major world power prior to Babylon was Assyria.
For a good overview of the decline of the Assyrian Empire refer to the Encyclopaedia Britannica (see article in Britannica CD 99: The History of Ancient Mesopotamia: Mesopotamia to the end of the: THE NEO-ASSYRIAN EMPIRE (746-609): Decline of the Assyrian empire). Here it describes how the Assyrian empire, after becoming weakened through civil war, fell to the combined forces of the Medes and the Babylonians, finally being extinguished in 609 BC. In this final battle, the Assyrians and the Egyptians fought side-by-side. Prior to being conquered by the Medes and Babylonians, the Egyptians fought against Judah - and Judah lost. This is the battle where Josiah was killed. The chronology of Judah places this event in 608 BC - but that is close enough to 609 BC when a 1 year margin of error is assumed.
The following time period emerges:
This is the proper fulfillment of Jeremiah's prophecy.
The seventy years is also referred to in Chronicles. This segment begins with Nebuchadnezzar carrying into exile the people of Judah after the destruction of Jerusalem in 586 B.C. - the third and final incident where people from Judah were taken into exile.
2 Chronicles 36:20-23 (NIV)
He [Nebuchadnezzar] carried into exile to Babylon the remnant, who escaped from the sword, and they became servants to him and his sons until the kingdom of Persia came to power. The land enjoyed its sabbath rests; all the time of its desolation it rested, until the seventy years were completed in fulfillment of the word of the Lord spoken by Jeremiah. In the first year of Cyrus king of Persia, in order to fulfill the word of the Lord spoken by Jeremiah, the Lord moved the heart of Cyrus king of Persia to make a proclamation throughout his realm and to put it in writing: "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. Anyone of his people among you--may the Lord his God be with him, and let him go up.'"
At first glance, this segment seems to imply that the desolation of Jerusalem would last 70 years. Read it again, and you will see that this is in fact not the case. This segment states that now that Jerusalem has been destroyed, the land would lay desolate at least until the seventy-year prophecy of Jeremiah was fulfilled. Jerusalem was destroyed in 586 B.C. The seventy-year prophecy ended with Babylon's fall in 539 B.C., and the people of Judah were allowed to return to Jerusalem by decree of Cyrus II in 538 B.C. So Jerusalem lay desolate from 586 - 538 B.C. - a total of 48 years.
The one other place where the seventy-year prophecy of Jeremiah is referred to is in the book of Daniel:
Daniel 9:1-3 (NIV)
In the first year of Darius son of Xerxes (a Mede by descent), who was made ruler over the Babylonian kingdom -- in the first year of his reign, I, Daniel, understood from the Scriptures, according to the word of the Lord given to Jeremiah the prophet, that the desolation of Jerusalem would last seventy years. So I turned to the Lord God and pleaded with him in prayer and petition, in fasting, and in sackcloth and ashes.
In this passage it also seems at first glance that Daniel believes Jerusalem would lay desolate for 70 years. But if this is the case, why is he so earnest in his prayer to God in behalf of his people. This segment comes in the first year of the rule of the Medes and Persians - i.e. 539/538 B.C. At this point, Jerusalem has laid desolate for only 48 years, so surely there would be another 22 years to go?
No, Daniel seems keen on the idea that the seventy-years is in fact now over and that the exiled people of Judah should return to Jerusalem as God had promised. This can only be the case if Daniel understood the seventy years as referring to the length of time that Babylon would rule, and not to the desolation of Jerusalem. So like the writer of Chronicles, Daniel understood that after Jerusalem was destroyed it would lay desolate for the remainder of the seventy-year period. Hence Daniel says that "the desolation of Jerusalem would last [the] seventy years." Now that the seventy years is up, Daniel is asking God "How much longer?" As it turns out, he had less than a year to wait until Cyrus II gave the decree allowing the people of Judah to return to Jerusalem.