Updated

The couple accused of kidnapping their two young sons and fleeing by boat to Cuba has been booked into a Florida jail after being handed over to U.S. authorities.

The Hillsborough County Sheriff's Office said on their website Wedneday that Joshua Michael Hakken and his wife Sharyn are being held at the Hillsborough County Jail on a number of charges, including kidnapping, child neglect and interference with custody.

Authorities say Hakken kidnapped his sons, 4-year-old Cole and 2-year-old Chase, from his mother-in-law's house north of Tampa last Wednesday. The boys' maternal grandparents had been granted permanent custody of the boys last week before Hakken allegedly kidnapped them.

On Tuesday, Foreign Ministry official Johana Tablada said in a statement that Cuba had informed U.S. authorities of the country's decision to turn over the couple and their children.

All four family members returned to U.S. soil Wednesday when their plane arrived in Tampa. The parents were handcuffed and separated from their children and each other during the flight, the Miami Herald reports.

After landing, the boys went through medical checks, which they passed, before being handed over to their grandparents, deputies told Fox 13.

The boys' grandparents, Bob and Pat Hauser, said they were thankful to the law enforcement agencies that participated in the search.

The return saga began on Sunday, when Cuba tipped the State Department off to the Hakkens' presence, and from that moment "diplomatic contact has been exchanged and a professional and constant communication has been maintained," Cuban Foreign Ministry official Johana Tablada said in a statement.

An AP reporter spotted the couple and the children beside their boat at the Hemingway Marina in Havana on Tuesday. A man who resembled photographs of Joshua Michael Hakken yelled out "Stop! Stay back!" as the reporter approached, but there was no outward sign of tension or distress between the family members.

The family showed no sign they knew a decision about their fate had been made. The four strolled by an outdoor restaurant as security officials kept reporters at a distance. The youngest child was seated in a stroller and the elder boy sat down on a curb.

The U.S. and Cuba share no extradition agreement and the island nation is also not a signatory of the Hague Convention on the Civil Aspects of International Child Abduction, an international treaty for governmental cooperation on such cases.

Cuba has harbored U.S. fugitives in the past, though most of those cases date back to the 1960s and 70s, when the island became a refuge for members of the Black Panthers and other militant groups. More recently, dozens of Cuban Medicare fraud fugitives in the U.S. have tried to escape prosecution by returning to the island.

But Cuba has also cooperated with U.S. authorities in returning several criminal fugitives in recent years, including Leonard B. Auerbach in 2008. Auerbach was wanted in California on federal charges of sexually abusing a Costa Rican girl and possessing child pornography. He was deported.

In 2011, U.S. marshals flew to Cuba and took custody of two American suspects wanted in a New Jersey murder.

Hakken lost custody of his sons last year after a drug possession arrest in Louisiana and later tried to take the children from a foster home at gunpoint, authorities said. A warrant had been issued for his arrest on two counts of kidnapping; interference with child custody; child neglect; false imprisonment and other charges.

According to the Hillsborough County Sheriff's Office, Hakken entered his mother-in-law's Florida house last Wednesday, tied her up and fled with his sons. Federal, state and local authorities searched by air and sea for a boat Hakken had recently bought. The truck Hakken, his wife and the boys had been traveling in was found Thursday, abandoned in Madeira Beach, Florida.

Authorities told Fox 13 that the family sailed through the Gulf of Mexico on the 25-foot sailboat to get to Cuba.

Terri Durdaller, a spokeswoman at the Florida Department of Children and Families, said it was not clear where the children will ultimately be placed.

"Louisiana is the ultimate decision maker on where these children will reside. It's likely they will be placed back in Florida with the grandmother," she said.

The family's flight to Cuba harkened back to the 1999 child custody case involving Elian Gonzalez, though unlike Gonzalez, the Hakkens had no apparent ties to the island.

In 1999, 5-year-old Gonzalez was found clinging to an inner tube off Florida after his mother and others drowned while fleeing Cuba toward American soil. The boy was taken to Miami to live with relatives, but his father in Cuba demanded the boy be sent back.

U.S. courts ultimately ruled Gonzalez should be sent back, though his Miami relatives refused to return him. In April 2000, U.S. federal agents raided the family's home and he was returned to Cuba soon after. He has since grown into a young man and joined a military academy.

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The Associated Press contributed to this report.