Domenico Rancadore, known as The Professor, was arrested after evading Italian authorities for 20 years.
The former Mafia fugitive was accused of fleeing Italy as he faced trial over his alleged role as a "man of honour" in the Cosa Nostra group.
He was convicted in 1999 of Mafia association and extortion in Trabia, near Palermo, and is wanted to serve a seven-year jail sentence.
The decision by senior district judge Howard Ribble to allow Mr Rancadore to walk free marks a dramatic turnaround, as the same judge had previously agreed to extradite him.
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