Steinberg was born in 1947 in a displaced persons camp in Hof, Germany. He immigrated with his parents as an infant to Israel (1949). His father, Rabbi Moshe Steinberg zt"l, served as the Rabbi of Kiryat Yam, and he spent a lot of time teaching his son Torah.
After graduating high-school Steinberg studied at the Rabbinic Academy Yeshivat Mercaz Harav Kook in Jerusalem. 
Steinberg studied medicine at the Medical School of the Hebrew University-Hadassah in Jerusalem and graduated in 1972. He trained in Pediatrics at the Shaare Zedek Medical Center in Jerusalem, and in Pediatric Neurology at the Albert Einstein College of Medicine & Montefiore Hospital Medical Center, Bronx, New-York. 
Steinberg has worked as a senior Pediatric Neurologist at Shaare Zedek and Bikkur Cholim Hospitals in Jerusalem, as well as in the various Sick Funds in Jerusalem. 
Steinberg served in the army as a medical officer in the Air Force, reaching the rank of Major.
Steinberg was the first director of the Schlesinger Institute for Medico-Halakhic Research at Shaare Zedek Medical Center, and the founder and first editor of the quarterly "Assia", devoted to issues in medicine and halakha.
Steinberg established and served as the Director of the Medical Ethics Center of the Hebrew University-Hadassah Medical School.
Steinberg submitted over 4,000 expert witness opinions in court cases in pediatric neurology and medical ethics.
Since 1969 Steinberg is researching and publishing extensively in the fields of general and Jewish medical ethics, history of medicine, medicine and law and pediatric neurology. He has written/edited 42 books and public reports in 65 volumes, 292 papers and chapters in Israeli and international Journals and books, and he has been lecturing Medical Ethics in the Hebrew University-Hadassah Medical School. He lectured at 250 national and international 

conferences, as well as numerous public lectures in 35 cities in Israel, in 32 cities in the USA and in 42 cities around the world.
His major, groundbreaking and monumental work is the 7-volume "Encyclopedia Hilchatit Refuit" (in Hebrew). This work was translated into English by Prof. Fred Rosner: "Encyclopedia of Jewish Medical Ethics", in 3 volumes. His Encyclopedia was the first ever put together on the subject.
In 1999 Steinberg received the most prestigious prize - The Israel Prize. He also received a variety of other prizes.
In 2008 Steinberg received Honorary Doctorate from Bar-Ilan University.
Steinberg has chaired several national committees on bioethical issues, including the National Israeli Committee for evaluation of living organ donors, the National Advisory Committee to the Minister of Health for Enacting a Law Concerning the Terminally-ill, the National Ethics Committee in accordance with the Dying Patient Act – 2005, the National Advisory Committee for Amendments of the Anatomy and Pathology Law, and the National Forum Concerning Organ Donations in Israel. He has also served as member in a variety of national and public committees and currently he is the co-chairman of the Israeli National Council on Bioethics.
Steinberg has served as an adviser on medical ethics issues to the Knesset and to the Chief Rabbinate of Israel. He also has been involved in halakhic aspects of modern medical issues with the most prominent Rabbinic authorities, particularly with Rabbi S.Z. Auerbach zt"l, Rabbi Y.S. Eliashiv zt"l, Rabbi O. Yosef zt"l and Rabbi E.Y. Waldenberg zt"l. 
Since 2006 Steinberg serves as the Director of the Yad Harav Herzog Institutes and as the head of the editorial board of the Talmudic Encyclopedia. 
Since 2013 a new project has been developed under his editorship – The Talmudic Micropedia. This is an abridged version of the Talmudic Encyclopedia, with additions of modern issues whenever related to the Talmudic entries. Steinberg serves as a member of the halachic committee of Magen David Adom, chairman of the Board of Mohalim of the Israeli Chief Rabbinate and the Ministry of Health, a member of the Committee for inter-religions dialogue of the Chief Rabbinate, and a member of the Committee for medical matters of the Chief Rabbinate of Israel.
Steinberg and his wife, Lynne, live in Jerusalem. They have three married children and thirteen grandchildren.