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Michel, 54, arrived on a private flight from Dubai, his lawyer Rosemary Patrizi told NDTV. Michel was arrested in the UAE last year on the basis of an Interpol notice and was out on bail.
The CBI said Michel's extradition took place "under the guidance" of National Security Advisor Ajit Doval.
The AgustaWestland case involves the deal to purchase 12 luxury helicopters for use by the President, Prime Minister, former prime ministers and other VIPs, when Manmohan Singh's Congress-led coalition was in power.
In 2014, the government scrapped the contract amid allegations that AgustaWestland, whose parent company Finmeccanica faced charges of bribery in Italy, had paid kickbacks in India.
The Enforcement Directorate has accused Michel of receiving 30 million Euros (about Rs 225 crore) from AgustaWestland as kickbacks.
Michel is one of the three middlemen being examined in the case, along with Guido Haschke and Carlo Gerosa.
In July, Michel's lawyer alleged that he was being pressured by Indian agencies to frame Congress leader Sonia Gandhi in return for amnesty from criminal proceedings.
In August 26, UAE had asked a court on the possibility of extraditing a British national to a third country. The court said a few days later that extradition is possible.
In November, a court confirmed the order, clearing the way for Michel's extradition to India.
On Monday, the Dubai government passed an administrative order to enable Michel's extradition.
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