Harrison was born in Alberta, Virginia, the son of Albertis S. Harrison Sr. and Lizzie, née Goodrich. He is related to Benjamin Harrison V and William Henry Harrison. He received an LL.B degree from the University of Virginia Law School in 1928.
Harrison married Lacey Virginia Barkley c.1940. They had two children, Antoinette H Jamison and Albertis S. Harrison III and 6 grandchildren, Albertis Sydney Harrison IV, Joseph D. Goodrich Harrison, Monica Harrison Kopf, Virginia Lacey Jamison Walter, James Carper Jamison II, Albertis Harrison Jamison.
Harrison went into legal practice in Lawrenceville, Virginia, where he became town attorney, before being elected commonwealth's attorney of Brunswick County.
He was elected to the Senate of Virginia in 1947. He served there for ten years, before being elected Attorney General of Virginia in 1957.
Harrison resigned as Attorney General in April 1961 to run for Governor, winning election that November with 63.84% of the vote, defeating Republican H. Clyde Pearson. His administration increased educational financing for new schools and laboratories and raised teachers' pay. He promoted the development of state-supported colleges and technical schools as well as improved vocational training. He helped to modernize state banking laws to attract investment and accelerated highway construction.
He sat on the Virginia Supreme Court of Appeals, later renamed the Supreme Court of Virginia, from 1968 to 1981. In 1968 he chaired the Commission on Constitutional Revision that drafted the 1971 Constitution of Virginia.
As Attorney General, Harrison was responsible for defending the state's resistance to school integration, as part of the Massive Resistance strategy endorsed and led by the state's political leader, United States Senator Harry F. Byrd.
Part of Massive Resistance involved the closing of public schools in various Virginia cities and counties to prevent racially integrated classrooms. Davis v. County School Board of Prince Edward County (1952) was one of the companion cases to Brown v. Board of Education (1954), but the Supreme Court had left enforcement to the local federal district judge. Moreover, the Gray Commission of Byrd loyalists had recommended passage of various laws to avoid or delay integration. After opinions by the Virginia Supreme Court on January 19, 1959 (the birthday of Robert E. Lee) as well as a three-judge federal panel overturned much of the new Virginia legislation, Governor James Lindsay Almond Jr. (previously attorney general) and Harrison decided not to defy those courts and allowed schools in Arlington and Norfolk to reopen. However the schools in Prince Edward County closed in 1958 and did not reopen until 1963, as white students used tuition grants to attend a private segregation academy at state expense, while black students were left to volunteer efforts. Other problematic school closures, ultimately opened pursuant to federal court orders included those in Albemarle, Warren County and later New Kent County (the subject of the 1968 Supreme Court decision in Green v. County School Board of New Kent County (1968). Harrison told the board to comply unless they were willing to risk prosecution. By this time, he, like a number of other Byrd Democrats, had concluded that obstinate resistance to integration could not continue.
Another aspect of Massive Resistance involved new laws regulating attorney ethics, designed to attack practices of the NAACP, which was pursuing the desegregation actions. Initially, the U.S. Supreme Court deferred to an upcoming decision of the Virginia Supreme Court about those new ethics rules in Harrison v. NAACP (1959), but the case came before it twice more in NAACP v. Button (1963) (which was reargued after Harrison resigned as Attorney General to run for Governor, and which Virginia lost under attorney general Robert Young Button.
Harrison died of a heart attack at his home in Lawrenceville on January 23, 1995. He is buried in Oakwood Cemetery in Lawrenceville, Virginia
The courthouse in Lawrenceville is named in his honor.