The ruling said, "Upon our thorough review of the record, we conclude that Davis has met the burden for a stay of execution," The Atlanta Journal-Constitution reported.
The ruling is the latest in a series of appeals for Davis, marking the third time in 16 months his scheduled execution was stayed.
Davis, 40, was convicted in the Aug. 19, 1989, murder of 27-year-old Savannah police officer Mark Allen MacPhail. Since the trial's conclusion, seven of nine key prosecution witnesses have recanted their testimony.
Davis' lawyers expressed relief about the appeals court decision.
"This is the first step toward a court hearing to consider the new evidence," attorney Jason Ewart said, "something we have been asking for for almost a decade now."
Davis asked the 11th U.S. Circuit Court of Appeals for permission to pursue litigation in federal court on his claims of innocence. The judges said the stay of execution is conditional and Davis must show he can meet the "stringent requirements" to pursue another round of appeals.