Rancadore, known as "The Professor", was arrested after evading Italian authorities for 20 years. The 65-year-old had been living quietly in the London suburbs.
Italian prosecutors accuse Rancadore of fleeing Italy as he faced trial over his alleged Cosa Nostra connections.
Senior District Judge Howard Riddle said he had based his decision on a ruling in a similar case by the Administrative Court, which has jurisdiction over lower courts in England.
However, Riddle changed his decision following a ruling last week by the Administrative Court, which binds lower courts in England, involving the court of Florence and a Somali man, Hayle Abdi Badre, who said his rights would be breached by prison conditions.
More From This Section
"The judgment of the Administrative Court is binding on me," Riddle said. "The higher court accepted that a similar assurance given in that case was in good faith, but was not sufficient."
Rancadore was convicted in 1999 of Mafia association and extortion in Trabia, near Palermo.
The Italian authorities want him to serve a seven-year jail term imposed in his absence in 1999.
In his judgment, Riddle said Rancadore "has been here for 20 years" and had a "long-standing marriage and children who are now adults".