The execution date was set after a Chatham County Superior Court judge signed Troy Anthony Davis' death warrant.
Mr. Davis, 38, is on death row for the Aug. 19, 1989, shooting death of Savannah Police Officer Mark Allen McPhail, who was killed while responding to an altercation.
Court records say Mr. Davis shot into a car in a Savannah subdivision and struck a man in the head, severely injuring him.
A few hours later, court records say, he struck another man in the head with a gun in a Savannah parking lot, where he soon encountered the officer.
Human rights groups have challenged Mr. Davis' conviction, citing race issues and witnesses who have since recanted their testimony.
One group, Amnesty International, said in a statement earlier this week that it believes Mr. Davis should be granted a new hearing by the U.S. Supreme Court, which on Monday refused to hear Mr. Davis' latest appeal.
The group said that Mr. Davis, who is black, was convicted of killing Officer McPhail, who is white, without any physical evidence.
Amnesty International also says several witnesses have implicated another man in the killing.
Previous appeals by Mr. Davis have failed.
His execution would be the second in Georgia this year. John Hightower was given a lethal injection Tuesday for killing his wife and two stepdaughters in Milledgeville in 1987.