Abraham Hoagland Cannon was born on March 12, 1859, to George Q. Cannon and Elizabeth Hoagland in Salt Lake City, Utah. As a youth, Cannon received a thorough education, graduating from Deseret University and studying the carpenter's and architect's trades. He also worked for a time on the Deseret News. On October 16, 1878, he married Sarah Ann Jenkins, and on October 15, 1879, he married Wilhelmina M. Cannon, his first cousin. Shortly before this second marriage, in October of 1879, Cannon was called on a mission to Europe for the Church of Jesus Christ of Latter-day Saints. He first went to England, then to Switzerland and Germany, and returned home to Salt Lake City in June of 1882.

On October 9, 1882, Cannon was called as one of the first seven presidents of the Seventies. During this time, he owned several bookstores and held managerial positions in several companies, including in the State Bank of Utah and in the Juvenile Instructor. He also wrote several books and articles throughout his life. During the government persecution of polygamists in the 1880s, Cannon helped hide his father, George Q. Cannon, and other apostles so they would not be charged. He himself was convicted of unlawful cohabitation on March 17, 1886, and served six months in the state penitentiary. On January 11, 1887, he married his step-sister Mary E. Croxall in Mexico, where polygamy was still legal.

Cannon was ordained a member of the Quorum of the Twelve Apostles on October 7, 1889, and soon after became the general manager of the Deseret News. Later he became the editor and publisher for the Contributor.

Abraham H. Cannon died unexpectedly of meningitis on July 19, 1896, in Salt Lake City, Utah. He was thirty-seven years old.