Rancadore, who was arrested in Britain last year after 20 years on the run, won his legal fight against extradition on March 17th on the basis that returning to Italy's overcrowded prisons would breach his human rights.
At a hearing in London on Thursday, the Crown Prosecution Service (CPS) confirmed that it had lodged an appeal but that it was not served within the statutory time limit and was therefore being withdrawn.
"You're free to go as far as this court is concerned," judge Quentin Purdy said.
Rancadore, 65, known as "The Professor", was sentenced in Italy in his absence in 1999 to seven years in prison for associating with the mafia.
When he was arrested in August, it emerged he had been living for the past 20 years in the London suburbs with his wife and two children, under a false name, Marc Skinner.
Rancadore was in court on Thursday to hear he was being freed. Dressed in a dark suit with gold buttons, striped tie and a white shirt, he said "yes, yes, thank you" before leaving the courtroom.
His wife Anne Skinner said she was "relieved to have her husband home".
"We're normal people. My husband really hasn't done anything wrong. He's not what he's been portrayed as," she said.
"We want to get our lives back and get back to normal. I want to be able to go into Sainsbury's (supermarket) and not be pointed at.
"I'm just happy he's home. He can go out and look after his garden now."