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 US authorities.

According to a website for the Hillsborough County Sheriff's Office, Joshua Michael Hakken and his wife Sharyn were being held at the jail on Wednesday on a number of charges including kidnapping, child neglect and interference with custody.

Cuba agreed to hand over the American couple on Tuesday. 

US diplomats in Havana said in a statement early on Wednesday that the two children had left Cuba and "are safely on their way home".

Officials in Florida have been searching for Joshua Hakken since last week when he allegedly broke into his mother-in-law's house near Tampa, tied her up and fled with his young boys.

Hakken lost custody of his sons last year and later tried to take the children from a foster home at gunpoint, authorities said.

The sheriff's office in Hillsborough County confirmed that Hakken lost custody of the children after being arrested in Louisiana on drug charges in June 2012, following what police described as "an anti-government rally".

Extradition issues

The US 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 harboured US fugitives in the past, though most of those cases date back to the 1960s and 1970s, 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 US have tried to escape prosecution by returning to the island.

But Cuba has also cooperated with US authorities in returning several criminal fugitives in recent years, including Leonard B Auerbach in 2008.

Source: Agencies