Lemons will succeed Chief Justice Cynthia Kinser, who will retire on Dec. 31. His four-year term will begin Jan. 1, 2015.
The court announced Lemons' election on Monday in a news release.
The General Assembly elected Lemons twice as a justice, in 2000 and in 2012. He had previously served as judge of the Court of Appeals of Virginia and as a Richmond Circuit Court judge.
Lemons also has served assistant dean and assistant professor of law at the University of Virginia School of Law.