ANSA said Vito Roberto Palazzolo was convicted in 2006 to nine years in prison for laundering money for mobsters.
International Business Times reported Palazzolo was implicated in the "Pizza Connection" and laundered money through New York pizzerias in the 1970s and 1980s.
The newspaper said the investigation of the "Pizza Connection" exposed a $1.6 billion heroin and cocaine smuggling operation.
Palazzolo's lawyer said his client will probably not appeal the decision.
The criminal court in Bangkok said the extradition will take at least 30 days.