The youngest of five children, Soloveichik was born to Rabbi Moshe Soloveichik in Khislavichi, Russia, at which time his father was the rabbi of that town. Rabbi Dr. Joseph Ber Soloveitchik (referred to, in Modern Orthodox circles, as "The Rav") and Dr. Samuel Soloveichik were his older brothers.
His family first moved to Poland in 1920. Before his father moved to New York in 1929, Rav Moshe engaged his student Rav Yitzchok Hutner to become Ahron's rebbe. Rav Ahron was Rav Hutner's first student. Ahron celebrated his Bar-Mitzvah in Warsaw, and then immigrated with his family to join his father in the United States in 1930. After he graduated from Yeshiva College, he went to law school at New York University (NYU) and graduated with a law degree in 1946. He then spent the next 20 years teaching at yeshivas in New York City.
Rabbi Soloveichik's first teaching position was in Mesivtha Tifereth Jerusalem then headed by Rabbi Moshe Feinstein, from whom he received his Semicha (Rabbinic Ordination). Shortly thereafter Soloveichik was appointed by Rabbi Yitzchak Hutner to give the highest daily lecture in Yeshiva Rabbi Chaim Berlin. Soloveichik's final position in New York was at Yeshiva University, where he instituted a popular weekly hashkafa class in addition to giving one of the advanced daily Talmud classes. It was during this time that Soloveichik was honored as Lecturer of the Year at YU, the first Rabbi to be so honored.
In 1966, he came to Chicago to head the Hebrew Theological College in Skokie. After differing with the administration there on certain key issues, he was let go in 1974 and began his own Yeshiva as the Rosh Yeshiva of Yeshivas Brisk (Brisk Rabbinical College) in Chicago, an American incarnation of the Brisk yeshivas and methods.
Soloveichik taught Torah for 58 years, the last 34 of which were in Chicago. He was well known for being a humble, kind man yet one with an iron will and unquestionable integrity. He was so well respected in the city of Chicago, that although he was the lone opinion against building an eiruv, (a halakhic boundary allowing carrying on Shabbos) they put off putting it up out of respect for him. Although the stroke he suffered in 1983 left him partially paralyzed, in nearly-constant pain and often in need of a wheelchair, he continued his duties at Yeshivas Brisk in Chicago and flew to New York every week to deliver a Talmudic lecture at Yeshiva University (a position he accepted after his older brother became ill and was unable to continue lecturing).
His wife, Ella Shurin, was a writer and teacher. The couple raised six children all of whom are rabbis or women married to rabbis: Moshe Soloveichik of Chicago, USA; Eliyahu Soloveichik of New York City, United States; Yosef Soloveitchik of Jerusalem, Israel; Chaim Soloveichik of Ramat Beit Shemesh, Israel; Rochel Leah Marcus of Toronto, Ontario, Canada; and Tovah Segal of Newton, Massachusetts, United States.
He was buried beside his wife Rabanit Ella Soloveichik and near his grandson Yisroel Yosef Soloveichik on the Mount of Olives in Jerusalem, Israel. His grandchildren include Rabbi Meir Soloveichik.
Other works in Hebrew include commentaries on the works of Maimonides (Parach Mateh Aharon) and the laws of mourning (Od Yisrael Yosef Beni Chai) which was dedicated in memory of his grandson who died young after a long battle with cancer.
Additional works in English include Logic of the Heart Logic of the Mind - Wisdom and reflections on topics of our times.HaDarom, No. 22, Tisrei 5726 (Oct. 1955): בענין קידוש החודש
HaDarom, No. 23, Nissan 5726 (April 1956): דין שימור במצות מצוה
Bais Yitzchak, 1987: בענין יהרג ועל יעבור