Domenico Rancadore was convicted by an Italian court in his absence in 1999 for being a member of the Sicilian Mafia, and was sentenced to seven years in jail.
A British judge had ordered his extradition in February.He had fought extradition since 2013, when he was found living in Uxbridge under the alias Marc Skinner.
The Italian Embassy said Rancadore's case "expired" last October.
Vincenzo Celeste, from the Italian Embassy, said while Rancadore's conviction for Mafia membership remained intact, Italian law states a sentence is considered expired once a period of more than double the time of the penalty has passed.
Karen Todner, Rancadore's solicitor, said the Italian Court of Appeal had agreed to extinguish the on-going case on 31 March.She said she was awaiting confirmation from the Italian Government that the European Arrest Warrant for him would also be dropped.
