The state Attorney General Bill McCollum's office said it would not challenge the court's decision.
Vicki Rios-Martinez, the victim's mother, was unhappy with the court ruling.
"This is like 16 years ago. Today was the same kind of emotions, the same kind of chaos, the same kind of roller coaster ride," she said. "The system has disappointed us over and over and over again."
Schwab was sentenced to death for the murder of 11-year-old Junny Rios-Martinez.
In March 1991, the month Schwab was released from prison on a sexual assault sentence, a newspaper published a picture of Junny for winning a kite contest.
He gained the confidence of Junny's family, claiming he was with the newspaper and was writing an article on the boy.
On April 18, he called Junny's school and pretended to be Junny's father and asked that the boy meet him after school. Two days later, Schwab called his aunt in Ohio and claimed that someone named Donald had made him kidnap and rape the boy.
He was later arrested and told police where he left Junny's body — in a footlocker in a rural part of Brevard County.
Schwab's execution was to be the first in Florida since the botched execution of Angel Diaz on Dec. 13. It took 34 minutes for Diaz to die — twice as long as normal — because the guards pushed the needles through his veins.