Vito Palazzolo had appealed against a previous extradition order from a Thai court in December 2012 after his detention in March of that year.
"It has been a very long procedure," Leonardo Agueci, the deputy chief prosecutor in Palermo in Sicily, was quoted by Italian media as saying.
Sicilian-born Palazzolo previously worked as a banker in Switzerland and was convicted in the 1980s of laundering mafia revenues from drug trafficking in an operation named the "Pizza Connection". He served three years in prison for the crime.
A few years after his release, the lead prosecutor in the case was assassinated with a roadside bomb that also killed his wife and three bodyguards.
Palazzolo is accused of being the "treasurer" for the last two godfathers of the Cosa Nostra who are now in jail – Bernardo Provenzano and Toto Riina, who imposed a reign of terror in the 1980s and 1990s.
An Italian court sentenced him in absentia to nine years in jail in 2009.
He had been living in South Africa under the name Robert von Palace Kolbatschenko before travelling to Thailand.
When he was sentenced, prosecutors in Palermo said Palazzolo was "one of the most important Cosa Nostra figures in 20 years, notably because of his key role between business and the mafia".
In South Africa – which declined to extradite him – Palazzolo was a major businessman with interests in mineral water, security and ostrich farming.
Investigators believe he also owns a diamond cutting business and a hunting ground popular with the rich and famous, and is an investor in a company in Angola specializing in precious stones.