The $750m (£485m) helicopter deal between India and Italy comes to a hold as charges emerge that Finmeccanica group paid bribes to win an Indian contract. India was to buy 12 helicopters from the Italian firm.
Giuseppe Orsi was arrested in Italy this week as part of a corruption investigation involving the sale of helicopters to the Indian government.
Finmeccanica has already handed the running of the firm to another director, Alessandro Pansa, while it deals with the allegations.
Mr Orsi announced his decision to resign in a letter, in which he denied any wrongdoing and said he had always worked "for the exclusive interest of Finmeccanica and its subsidiaries".
He said he wanted to "help to calm the atmosphere" at Finmeccanica by resigning.