Joshua and Sharyn Hakken allegedly kidnapped their sons, Chase, 2, and Cole, 4, from their grandmother's Tampa, Fla., home last Wednesday, leaving the woman tied up.
The couple then traveled to Cuba on their sailboat where they were spotted. Cuban authorities turned the family over to the U.S. State Department and the FBI, CNN reported.
The couple face a federal charge of unlawful flight to avoid prosecution and state charges of kidnapping and interference with child custody. Joshua Hakken also faces charges of false imprisonment, burglary, battery and grand theft auto, Hillsborough County Sheriff David Gee said.
The children were expected to have a medical exam before being returned to their grandparents, Bob and Patricia Hauser, who have had custody since earlier this month, CNN reported. Gee said the boys appear to be healthy.
The Hausers were given custody of the boys after Louisiana police discovered the Hakkens in a hotel acting strangely and possessing drugs and firearms last June, CNN reported.
"When police arrived, both Mr. and Mrs. Hakken were acting in a bizarre manner that alarmed officers. They were talking about 'completing their ultimate journey' and were traveling across the country to 'take a journey to the Armageddon,'" Slidell police said in a statement. "Let it be noted that both of their children were present in the hotel room at the time."
Joshua Hakken was arrested on drug charges and the couple were stripped of custody of their children.