France has extensive experience in the criminal justice sector and is the non-executive chair of the Office for Legal Complaints.
The organisation is responsible for regulating the private security industry in the UK, including doorstaff.
Bill Matthews has been re-appointed as the Board member with particular responsibility for representing Scottish interests.
Home Office minister for criminal information Lord Taylor said: “I am very pleased to announce Elizabeth France as the chairman of the SIA.
“With extensive experience within the police and security sector, Elizabeth has just what it takes to drive the Authority forward.
“I would also like to thank Bill Matthews for his significant contribution as interim SIA chairman over the last 12 months.”
France’s term as chair runs for three years.