Haber was born in Tel Aviv in 1940. At the age of nine he began writing for the children's edition of HaTzofe and later for the youth edition of Herut newspaper. At the age of fourteen he became a member of the Herut staff. In 1958 he was drafted to the IDF and was posted as a reporter for the Bamahane military newspaper. During his service he met and befriended the commander of the Northern Command, Yitzhak Rabin.

On his discharge from the IDF in 1960, he joined Yedioth Ahronoth as a correspondent on military issues. He was also an investigator for several Israeli television programs and edited and presented radio programs on Israel Army Radio.

In late 1985 he was appointed by Rabin, then Minster of Defense, to be his special media adviser. After Rabin's withdrawal from the government in 1990, he returned to Yedioth Ahronoth. When Rabin was elected Prime Minister in 1992, he was appointed to be an adviser and bureau chief. He wrote many of Rabin's speeches, was part of the team that secretly negotiated the Israel-Jordan Treaty of Peace, and organized Rabin's official travels abroad, including to the Oslo Accords and Rabin's reception of the Nobel Prize for Peace.

On the night of 4 November 1995, he was the one to announce the official government statement regarding Rabin's death:

The government of Israel announces in dismay, in great sadness, and in deep sorrow, the death of prime minister and minister of defence Yitzhak Rabin, who was murdered by an assassin, tonight in Tel Aviv. May his memory be blessed.

After Rabin's death, he returned to his journalistic career. In addition, his business activities include: President and CEO of Geopol Ltd. since 1996. Since 2001, he also has served as CEO of Kavim Ltd., and is a member of the board of directors of Africa Israel Ltd. and "Israel Experience Co."; Since 2002, he has been a director of Ampal Ltd. He is also a board member of the Jewish Agency for Israel.

He wrote several books, often with other writers, such as Michael Bar-Zohar, Ze'ev Schiff, Yossi Melman and Ehud Ya'ari.