The move marks the first time a governor has asked for genetic testing of someone already put to death.
The testing comes in the case of Roger Keith Coleman, a convicted killer whose proclamations of innocence sparked concern nationwide over whether the wrong man died in Virginia's electric chair.
"We have found that the latest DNA technology -- in certain instances where the other facts of a case support it -- has provided a definitive result not available at the time of trial or post-conviction testing," Warner said in a statement.
Coleman was convicted and sentenced to death for the 1981 brutal rape and stabbing of his sister-in-law, 19-year-old Wanda McCoy.
The tests, on vials of evidence that have been preserved for years at a California laboratory, are being conducted at the Center of Forensic Sciences lab in Toronto, Ontario. Results could be announced before Warner leaves office next week.
Boston schools pull out free condoms over wrapping complaints
Aaron Carter is still in love with Hilary Duff