Alexander Jackson, Sr., was born in Dublin, Ireland, in 1786 and immigrated to the United States with his brother Humphrey Alexander in 1808. Both men were members of Stephen F. Austin's Old Three Hundred colonists. Alexander was granted two leagues of land, to which he received title on July 16, 1824. The lower league began on the east bank of the Colorado River and continued north; the upper league ended a short distance across West Bernard Creek. Originally the land was in Colorado County, but when Wharton County was established in 1846, both leagues were within the new county.
The Jackson brothers' father was a member of the Irish Parliament, and both men were actively engaged in prerepublic Texas politics. Alexander counted among his friends William Kincheloe and Aylett C. Buckner, other activists. Inhabitants of the Colorado District met at the Jackson home on December 15, 1823, to elect militia officers for that district. Jackson's home was situated near a crossing of Peach Creek, next to the eastern boundary of his land and a short distance from Kincheloe's home.
The 1823 census of the Colorado District lists Jackson's family as his wife, Ann, and his four children. In August 1824 Stephen F. Austin spent the night with Jackson to discuss an Indian campaign against the Karankawas below Bay Prairie. That summer Jackson had received an arrow wound in his elbow during a skirmish with the Indians, in which John C. Clark, Amos Rawls, and Robert H. Kuykendall took part. In 1825 Jackson and Buckner were accused of being perverse and insubordinate, and Austin sent word to the sheriff of the area to order Jackson, Buckner, Kincheloe, Clark, Kuykendall, and several others to report to San Felipe on June 1825 and give evidence in the case of reported seditious conduct. No one appeared to testify and the charges were dropped. In April 1826 Lt. Rawson Alley exempted Jackson from company muster, but not from campaign duty against an enemy, due to a physical inability. On January 4, 1827, Jackson and forty-eight other men attended a meeting in the home of Bartlett Sims on Peach Creek. All men present signed a declaration of loyalty to the Mexican government and condemned the Fredonia Rebellion.
Jackson died sometime during 1829, and his farm was advertised for rent in the Texas Gazette in 1830. The two leagues were divided into three lots running their length from the Colorado towards West Bernard Creek. Jackson's heirs were his three surviving children.