Mr Green, who was the chief executive of the Australian Private Equity & Venture Capital Association (AVCAL) for seven years, will start in his new role on 8 April 2015.
Stockbrokers Association chairman Karl Morris said Mr Green's "experience and formidable contacts" would continue to raise the profile of the association.
"Andrew will also provide our members with a meaningful, powerful and respected voice on industry matters as well as show the wider community how the profession can deliver them a more prosperous future through research, advice and wealth management services," Mr Morris said.
For his part, Mr Green said be would be seeking further engagement for the association with members, regulators and other market participants.
"My role will be to further strengthen the profession and continue to promote, largely through our highly credentialed and well-recognised educational workshops, the high standards, skills and knowledge of broking professionals," Mr Green said.
Commenting on the departure of former chief executive David Horsfield, Mr Morris wished him "all the best for the future".
"David has been a tireless advocate on behalf of the Stockbrokers Association in his role as CEO for the past 12 years," he said.
Mr Green's appointment was made after the Stockbrokers Association employed Horsley & Company to undertake an recruitment search on its behalf.
