Authorities say Hannon and two other men went to the Cambridge Woods apartment of 27-year-old Brandon Snider and 28-year-old Robert Carter on January 10, 1991. One of the other men stabbed Snider several times when he answered the door. Hannon then cut Snider's throat.
Carter, who also lived in the apartment, tried to hide under a bed, but Hannon followed and fatally shot him six times.
Authorities believe revenge was the motive for the killings. Investigators say Snider returned home to Indiana shortly before he was killed and threatened his ex-girlfriend, the sister of one of the men with Hannon.
The Florida Supreme Court refused to block Hannon's execution last week. Hannon's attorneys argued that his execution should be stopped for several reasons. The court rejected those arguments.
Justice Barbara Pariente dissented saying the jury was not properly presented with information about Hannon's background before recommending a death sentence. The jury had voted unanimously to sentence Hannon to death.
Before the murders, Hannon served over two years in prison for the crimes of burglary, grand theft and cocaine possession he committed in the late 1980s.