Yuli Edelstein was born in Chernivtsi in the Soviet Union (now Ukraine) to a Jewish family. His mother, Anita Edelstein was Jewish, while his father, Yuri Edelstein, is the son of a Jewish father and Christian mother. Both converted to Christianity, and Yuri is now a Russian Orthodox priest in Karabanovo of Kostroma Oblast named Father Georgy. While his parents taught at universities in the countryside, Edelstein was raised by his maternal grandparents. His grandfather had taught himself Hebrew at the age of 70 and used to listen to the Voice of Israel on a shortwave radio. When Edelstein's grandfather died, Yuli began to study Hebrew and read books such as Exodus by Leon Uris, which inspired him.
In 1977, during his second year of university, Edelstein applied for an exit visa to immigrate to Israel. Turned down, he began to associate with a small group of Hebrew teachers who held classes in their apartments.
In 1979, he was expelled from the university and suffered harassment by the KGB and local police. During this time, he found odd jobs as a street cleaner, security guard, and more.
In 1984, he and other Hebrew teachers were arrested on fabricated charges, Edelstein himself being charged with possession of drugs, and sentenced to three years. He was then sent to Siberian gulags and did hard labor, first in Buryatia and then in Novosibirsk. He broke several bones after falling from a construction tower. He was due to be transferred back to Buryatia, but his wife, Tanya, threatened to go on hunger strike if he was returned there.
Edelstein was released in May 1987, on the eve of Israeli Independence Day, the next to last of the refuseniks to be freed. He then immigrated to Israel, moving to the West Bank settlement of Alon Shvut. He did his national service in the Israel Defense Forces, attaining the rank of Corporal.