Chavez said nothing before he was given a lethal injection shortly after 8 p.m., the Miami Herald reported. He left a rambling written statement that hoped for God's love "for those who in their pain desire my death" but neither apologized to Jimmy's family nor claimed innocence.
The execution was delayed for two hours while the U.S. Supreme Court considered a final appeal.
Don Ryce, 70, Jimmy's father, and the victim's brother, Ted, witnessed the execution. Don Ryce has become a crusader against child molesters and read a statement to reporters after the execution warning people who kill children.
"People will not forget, they will not forgive," Don Ryce said. "We will hunt you down and we will put you to death."
Prosecutors and police detectives involved in the case that shocked the Miami area also watched as Chavez died. One juror from his trial also attended.
"It's closure. Justice has been served for an evil man," Pat Diaz, the retired Miami-Dade police detective who led the investigation into Jimmy's murder, told the Herald.
Chavez was pronounced dead at 8:17 p.m., Florida State Prison officials said.
Jimmy's mother, Claudine, died of a heart attack in 2009 at age 66. Hi sister, Martha, took her own life in Atlanta on Dec. 30, 2012, at the age of 35.
Jimmy disappeared in 1995 after getting off a school bus in a rural area of Dade County. Chavez, who had left Cuba on a raft and worked at a horse farm, became a suspect three months later when his employer, searching his trailer for property she believed he had stolen, found a backpack like the one Jimmy had been described as carrying.
Florida has executed 12 people since 2012.
Celebrity Families of 2014 [PHOTOS]