"I've got my man," Citrus County Sheriff Jeff Dawsy told a news conference.
Dawsy said John Evander Couey confessed to investigators after taking a lie-detector test.
"The FBI sent their polygrapher up there that did the polygraph. John Couey was polygraphed today and at the end of the polygraph he says 'you don't need to tell me the results, I already know what they are, could I have the investigators come back in?' And the investigators came back in. He apologized to the investigators for wasting their time,'' said Dawsy. "John Couey admitted to abducting Jessica and subsequently taking her life."
The sheriff said Jessica Lunsford's body had not been found, but Couey gave them a general area to search, reports CBS' Alison Harmelin.
Couey, 46, was arrested in Augusta, Ga., on Thursday on a probation violation for failing to notify officials that he was moving, a requirement for sex offenders.
He had waived extradition and was cooperating with detectives during interviews Friday, but he had not been charged in Jessica Lunsford's February disappearance, authorities said.
"He's not going anywhere up there,'' Dawsy said. "He's on a no-bond, and we will bring him back when we do everything correct. And we talked about building a case, and this is not a time to sing anybody's praises, but I will tell you we've built a case, a very methodical case. And, I've got my man."
Authorities cordoned off an area Friday near the home of Couey's half-sister, who lived about 150 yards from the home Jessica shared with her father and grandparents. Dawsy would not comment on what investigators were doing in the area, but said it "will take hours." Police had yet to recover a body.
A sheriff's spokeswoman who answered the phone at the Lunsford home Friday evening said the family declined to make any immediate comment. Jessica's father, Mark Lunsford, has said the family did not know Couey.
Jessica's stepfather, Lonnie Bryant, told The Associated Press by telephone from Ohio that he and the girl's mother, Angela Bryant, planned to come to Florida soon.
"I'm going through agony right now," he said.
Couey's home in Homosassa is about two miles from Jessica's, but he sometimes stayed with his half sister, about 150 yards from the girl's house, Sheriff Dawsy said.
Couey left Florida on or about March 4, about a week after the girl's disappearance, after telling relatives that police would be looking for him.
Jessica, a third grader, was last seen when she went to bed Feb. 23 in the home where she lived with her father and grandparents. She was discovered missing the next morning, with an unlocked door and a missing stuffed animal serving as evidence of her disappearance.
Couey's criminal record includes arrests for burglary, carrying a concealed weapon and indecent exposure. In 1991, he was arrested in Kissimmee on a charge of fondling a child under age 16. Records don't show how the case was resolved.
During a house burglary in 1978, he was accused of grabbing a girl in her bedroom, placing his hand over her mouth and kissing her, Dawsy said. Jessica was last seen in her bedroom, Dawsy has said. Couey was sentenced to 10 years in prison but was paroled in 1980, a time when inmates were serving a small fraction of their sentences.
George Kanaris, 46, owner of Emily's Family Restaurant about a mile from the Lunsford home, said Couey worked there as a dishwasher more than 10 years ago, from about 1992 to 1994.
Kanaris said he fired Couey because he wrote a romantic letter to a bus girl who was 14 or 15.