George A. Smith was born in Potsdam, St. Lawrence County, New York, the son of John Smith and Clarissa Lyman, and was brought up in the Congregational Church. His first cousin was Joseph Smith, Jr., the founder of the Church of Jesus Christ of Latter-day Saints or Mormon Church. In September 1832, at the age of 15, George A. Smith, was baptized into the new church, eight months after his parents had been baptized.. The following year, John Smith and his family moved to Kirtland, Ohio, the church's new headquarters. There George met his cousin, Joseph, for the first time. In 1838, he moved with his parents and a large body of church members to the state of Missouri.

In the spring of 1834, the 16-year-old Smith accompanied a group of Latter Day Saints on a 2000-mile march to Missouri and back to Ohio. This trip, known as Zion's Camp, was intended to bring aid to suffering members of the church in Missouri. Smith served as a missionary to the eastern United States, traveling and preaching during the summers of 1835, 1836, and 1837, while attending school each winter.

Smith was ordained a seventy in the priesthood on March 1, 1835, by Joseph Smith. On April 26, 1839, at the age of 21, George A. Smith was ordained an apostle and became a member of the Quorum of the Twelve. Future church President Wilford Woodruff was ordained an apostle on the same day. The two men replaced former apostles Thomas B. Marsh, who had left the church, and Orson Hyde, who had been disfellowshipped and removed from his position.

Isaac C. Haight, Cedar City stake President, and second in military command under Dame, met with Smith again on August 21. Haight told Smith he had heard reports that 600 troops were already approaching Cedar City from the East, and that if the rumors were true, Haight would have to act without waiting for instructions from Salt Lake City. Smith agreed, and "admired his grit". Smith later said he was uncomfortable, perhaps "on account of my extreme timidity", because some of the militia members were eager that "their enemies might come and give them a chance to fight and take vengeance for the cruelties that had been inflicted upon us in the States", such as the Haun's Mill massacre, where 18 Mormons were killed in 1838 in a skirmish with the Missouri militia during the Mormon War.

After Joseph Smith's death and the assumption of church leadership by Brigham Young, George A. Smith traveled to the Salt Lake Valley as a Mormon pioneer with the first company of settlers in 1847. In the winter of 1850, Smith led a company of 118 volunteers and about 30 families to establish a colony near the Little Salt Lake in Iron County. They arrived at Center Creek, 265 miles from Salt Lake City, on January 13, 1851. Under direction from the General Assembly of the State of Deseret, the group organized the political entity of Iron County and elected Smith as chief justice. During the winter of 1850–51, the settlers constructed a fort enclosing homes, a meeting house, a school, and a watch tower. They named their community Parowan. Smith taught school during the first winter, and later served as a member of Utah's territorial legislature.

Smith was the eighth official Church Historian and General Church Recorder of the LDS Church between April 1854 and 1871. In 1873 he was appointed and sustained as Trustee-in-Trust for the church, which office he held until his death.

On August 25, 1857, Smith's group camped next to the Fancher–Baker party, headed the opposite direction, at Corn Creek, now Kanosh. Smith later said he had no knowledge of the Baker–Fancher party prior to meeting them on the trail. When the Baker–Fancher party inquired about places to stop for water and grazing, Hamblin directed them to Mountain Meadows, near the "Indian farm" there, a regular stopover on the Old Spanish Trail.

In 1868, Smith was called to replace Heber C. Kimball as First Counselor in the First Presidency to church President Young. Smith served in this position until his death in 1875. Smith's first wife, Bathsheba W. Smith, served as general President of the church's Relief Society from 1901 to 1910. A son, John Henry Smith, also served as an apostle and member of the First Presidency. George A. Smith's grandson and namesake, George Albert Smith, also became an apostle and later was the church's eighth President.