Jamieson, Fausset and Brown on Jeremiah 16:19-20

19-20. The result of God's judgments on the Jews will be that both the Jews when restored, and the Gentiles who have witnessed those judgments, shall renounce idolatry for the worship of Jehovah. Fulfilled partly at the return from Babylon, after which the Jews entirely renounced idols, and many proselytes were gathered in from the Gentiles, but not to be realized in its fulness till the final restoration of Israel (Is 2:1-17).