Edelstein was born in western Ukraine. Because of his efforts to emigrate to Israel he was put in Gulag labor camps in Siberia for three years. After this time he made Aliyah (emigrated to Israel) in 1987.
With fellow refusenik Nathan Sharansky he founded the political party of Yisrael BaAliyah ("Israel on the Up") in 1996. The same year he entered the Knesset.
From 1996 to 1999 he was also minister of immigration absorption in the First Netanyahu Government, and from 2001 to 2003 also deputy minister of immigration absorption in the First Sharon Government.
In 2003 Yisrael BaAliyah became part of HaLikud and Edelstein became an MK for this party. In 2006 he lost his seat but in 2007 he returned.
From 2009 to 2013 he was also minister of information and diaspora in the Second Netanyahu Government.
Since May 17, 2020 he has been minister of health in the Fifth Netanyahu Government.
Although Edelstein thinks that Israelis and Palestinians can peacefully live together he is negative about the establishment of an independent State of Palestine because he is afraid it will attack Israel.
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