State court Judge Robin Reese signed the warrant Friday morning in a Salt Lake City courtroom.
The 49-year-old Gardner has been on Utah's death row for 25 years. After Reese said Gardner's avenues for appeal are exhausted and that he would sign the warrant, Gardner said "I would like the firing squad, please."
Gardner would be the first death row inmate executed since Joseph Mitchell Parsons died by lethal injection in 1999.
Gardner was sentenced to death in 1985 for the Salt Lake City courthouse slaying of attorney Michael Burdell during a failed escape attempt.
Gardner's attorney says an appeal is planned.
