Teller was born in Vienna, Austria to Shlomo Teller, an American soldier who helped the government capture and punish Nazis. After WWII, Shlomo began to design clothes for a living in Austria. Hanoch was raised in Stamford, Connecticut. He received his bachelor's degree in liberal arts from Yeshiva University of New York, and continues to study at the Mir Yeshiva in Jerusalem. He received rabbinic ordination from the previous Rav of the Kotel, Rabbi Meir Yehuda Getz.

He and his wife, Aidel, have 18 children. They reside in the Arzei HaBira neighborhood of Jerusalem.

Teller began his writing career penning articles for The Jewish Observer, Moment Magazine, The Jerusalem Post, and Jewish Women's Outlook. He received the Jerusalem Award of 5742 (1982) in an international essay competition marking the fifteenth anniversary of the re-unification of Jerusalem.

His first series of books, Once Upon a Soul, Souled! and Soul Survivors, introduced the genre of true, contemporary stories promoting the themes of hashgacha pratis (Divine Providence) and human kindness. Teller later branched out into biographies of contemporary Orthodox Jewish personalities — such as Rabbi Shlomo Zalman Auerbach, Rabbi Levi Yitzchak Horowitz, Baltimore Torah day school principal Rabbi Binyamin Steinberg, and Toronto philanthropist Joseph Tanenbaum — using anecdotes as the vehicle for moral and ethical lessons.

A large section of his corpus presents stories on specific ethical concepts, such as: judging others favorably (Courtrooms of the Mind), integrity (Above the Bottom Line), avoiding argumentation and strife (Give Peace a Stance), and the impact of a small positive gesture (It's a Small Word After All). Several of his books have been translated into Hebrew, Russian and Spanish.

Teller is a popular speaker for schools, women's groups, synagogue functions, learning seminars, fundraising dinners, and organizational meetings in North America, South America, Europe and Israel. He is known to have taught over 800 students a week in his prime.

He is an instructor at Yeshivat Hakotel for men and teaches at numerous Jerusalem women's colleges. He is a faculty member of Michlelet Mevaseret Yerushalayim College of Jewish Studies for Women, Darchei Binah Women's School, Afikei Torah Women's School for Advanced Torah Studies, Midreshet Moriah, Michlala-Jerusalem College, Bnot Torah Institute, Neve Yerushalayim Institutes, Naaleh Online Torah School, and others.

Teller is an independent guide licensed by Yad Vashem to lead tours in its new Holocaust Memorial Museum. He leads tours combining his knowledge of the sites and events of the Holocaust with stories describing the experiences of individual victims, and produced an eleven-part CD lecture series on the subject (Comprehending the Incomprehensible: The History, Heroism and Lessons of the Holocaust.

In the late 1990s, Teller produced a docudrama exploring miracles in everyday life (Do You Believe in Miracles?).

Teller is very involved with the promotion of American Republicanism which led him to support Al Gore and and Teller's friend Joe Lieberman in the 2000 presidential elections. Also, Rabbi Teller is close friends with Michael Medved, a conservative radio personality.