Mr Johnson, who is a former managing director of the firm, will officially leave the board in July after two decades of service.
His decision follows those of Bill Moss, who retired from his post as group head of Macquarie's banking and property operation, and executive chairman David Clarke, who has stepped down to take a role as non-executive chairman.
It is thought that Mr Johnson will remain in his position of chairman of the Asia-Pacific Economic Cooperation Business Advisory Council, and of AGL Energy and EngeneIc.
However, shareholders and market analysts have welcomed the changes and do not anticipate the changing of the guard to alter the company's current expansion strategy.
David Walsh of Barclays Global Investors, which owns a stake in Macquarie, told Reuters: "There is a lot of talent in there and there is a lot of planning going on.
"And probably it is a good thing that people who have been around for long and have seen the business grow to that level think it is time to hand over to somebody else," he added.
Macquarie is the largest investment bank in Australia and employs 10,000 people worldwide.