Spanish waiter Francisco Montez is accused by the French authorities of raping and murdering the 13-year-old Cornish girl while she was on a school trip to Brittany in 1996.
On Tuesday, a judge in Miami, Florida ordered that he should be extradited to France to stand trial, after DNA tests linked him to the scene of the crime.
Under US law, Montez has the right to appeal every decision right up to the Supreme Court in Washington - a process which lawyers say could take up to two years.
Mr Montez is also unlikely to go anywhere until after he stands trial in US on charges of burglary and lewd conduct, scheduled to begin on 2 July.
US judge Stephen Brown said there was "probable cause" Mr Montez had committed the murder.
Assistant US attorney Louis Perez added: "He will not be put on a plane until the state matter is concluded."
DNA tests in America showed a 100% match with genetic material found at the scene of the crime and the match was confirmed by French authorities in separate tests, prompting them to issue a 17-page international arrest warrant.
Appeal expected
The judge rejected a challenge by lawyers for Mr Montez over the reliability of the DNA evidence, saying that was for a trial in France to decide.
He said he would not issue an extradition order before Monday.
Speaking from France, the Dickinson family's lawyer, Herve Rouzaud-le-Boeuf told BBC News 24 that Caroline's father John "was extremely happy with the quick decision of the judge".
The extradition process is further complicated by the forthcoming US trial.
The 51-year-old restaurant worker, from Asturias in Spain, was arrested in March after allegedly breaking into a woman's apartment and attempting to commit what is described as a lewd and lascivious act while she slept.
If he is sentenced in the US, it will be up to that country's justice department and immigration authorities to decide if he should serve it before being sent to France or can complete his sentence in a prison there while awaiting trial.
In March he was also named in court by a French judge as a chief suspect in the Dickinson case who was "particularly" wanted by police from a list of around 50 people sought for questioning.
Extensive DNA tests
The US authorities only considered his possible link with the Dickinson case after US immigration officer Tommy Ontko had read about the schoolgirl's murder while on holiday in Britain.
At an inquest into Caroline's death in Cornwall in April, two of her school friends described how they were disturbed by noises coming from Caroline's bed but went back to sleep thinking she was having a bad dream.
Her lifeless body was discovered in the dormitory the next morning.
Extensive investigations by the French authorities have involved the DNA testing of more than 3,500 men in the search for Caroline's killer.