Raymond Roth, 47, made the admission to a traffic cop in Santee, S.C., after being pulled over for speeding while headed north on Interstate 95.
The officer ran Roth's name through a national database during the 3:30 a.m. stop and learned he was listed as missing in New York, said Santee Police Chief Bing Jones.
"He told the officer that he was having some problems in New York, so he went off to Florida," Jones said. Roth had recently been laid off, police said, and neighbors said he put his home up for sale last week.
The feared drowning Saturday triggered a massive search until Wednesday, when a relative told authorities Roth was in Florida, State Park Police said.
Shortly after getting the speeding ticket, Roth called State Park Police himself Thursday to say he was returning to Long Island, according to Capt. Bruce Marx.
"I have spoken to him, and he advises that he is coming back and will let us know when he does," Marx said.
Late Thursday night, Roth hadn't contacted authorities on Long Island or arrived at his home.
He wasn't detained in South Carolina, Marx said, "because it's not a crime to be missing."
Police said they have spoken "several times" to Roth's wife, Evana, who said she had "absolutely no knowledge" of a faked drowning. At about 10:30 Thursday night, state park police detectives were at Roth's Massapequa home to speak with her again. Roth hasn't admitted to faking his death, and police are still trying to piece together what happened after he was reported missing, including if Roth even was at Jones Beach that day.
Detectives have talked to family members to make arrangements about what might happen when, or if, Roth returns, Marx said.
The Nassau County district attorney's office said in a statement that prosecutors are "monitoring the police investigation into this matter. It's premature to comment as to whether crimes were committed."
Authorities searched nearly four days for Roth after his adult son told authorities he had entered the Atlantic Ocean near Field 6 at Jones Beach and disappeared.
Marx told Newsday on Saturday that Roth's son saw his father swim straight out and said he then lost sight of him.
Police were told Roth was last seen swimming east of Field 6 about 3:30 p.m. in an area not watched by lifeguards.
Police first learned Roth was alive and well when his brother, who lives in Long Beach, called them Wednesday to say he had heard from Roth.
At that time, police called off the search, which had included Nassau County police and the Coast Guard, and contacted the Orange County sheriff's office outside Orlando, Fla., in an unsuccessful attempt to track down Roth.
Roth had fallen on hard times. He recently had been laid off by an international computer firm, police said. No one answered the door Thursday at his two-story home, where a "For Sale" sign hung in the front yard.
Jane Stone, who has lived on the block for more than 50 years, said Roth fixed up the house this summer, doing the brickwork in the yard.
"He was really proud of it," she said. "He said, 'Do you want to come in and see the backyard?' It was beautiful."
The four-bedroom, two-bathroom house is on the market for $549,999, according to the Multiple Listing Service of Long Island.
Another neighbor, Ron Christian, 64, said he saw Roth and his son headed to the beach last week and all seemed normal.
With Zachary R. Dowdy,
Ann Givens, Alison Barnwell, Scott Eidler and John Valenti