Parkinson's appointment follows Matthew Comyn's decision to leave his post as MSSB chief and return to Commonwealth Bank of Australia (CBA) after only five months in the role.
Joining MSSB in 2006, Parkinson was state manager for Melbourne and prior to that spent time as chief executive of the Bendigo Stock Exchange.
He also spent time at ANZ Securities.
"Harry has 20 years of experience in the industry and has done a great job building up the business in Melbourne, as well as around Australia. Aside from that, the business is continuing to move forward," an MSSB spokesperson told IFA.
Comyn, who began in the role in late February, joined from Commonwealth Securities, where he was managing director.
A CBA spokesperson said Comyn was a highly-talented performer and the group welcomed him back, but declined to comment on what role Comyn would take.
When Comyn joined MSSB he succeeded Tom Burns, who left to work with the group in the United States.
CBA general manager of credit cards Stephen Karpin was appointed to Comyn's former role at Commonwealth Securities in March.
Morgan Stanley assumed management control of MSSB in June last year and has been undertaking a comprehensive development plan for the business in Australia.
The group reported that the plan had also resulted in a significant number of financial advisers joining the firm.
