Lord Nimmo Smith has served as an insolvency Judge and was one of five judges who heard the appeal of Lockerbie bomber Abdelbaset al-Megrahi in 2002.
The SFA announced the inquiry on Friday - three days after Rangers went into administration.
The probe will focus specifically on whether there have been any breaches of their Articles of Association, relating to rules regarding whether club officials are "fit and proper" to hold such positions.
The SFA announced their independent panel would also include Professor Niall Lothian, a past president of the Institute of Chartered Accountants of Scotland and Bob Downes, who is deputy chairman of the Scottish Environmental Protection Agency.
SFA chief executive Stewart Regan will also sit on the panel.
The governing body revealed that Regan met Lord Nimmo Smith on Tuesday to define the terms of reference for the investigation.
The inquiry team have been handed the same powers as the SFA to investigate the potential breach of their rules and have been asked to report to the board within two weeks.
Regan said: "I am delighted Lord Nimmo Smith has agreed to chair the independent inquiry.
"I am certain the experience contained within the panel will enable us to achieve more clarity on the situation regarding Rangers FC.
"There will be no further comment on the investigation until it is complete and its findings presented to the board."
The SFA launched the independent inquiry after being frustrated in attempts to secure clarity regarding Rangers owner Craig Whyte's previous business experience.
The governing body contacted Rangers on December 1 to seek clarification after the club confirmed Whyte was previously disqualified as a company director for seven years from 2000.
The SFA said their efforts to obtain information on Whyte had been "restricted by the club's solicitors' continued failure to share information in a timely or detailed manner".
The SFA Articles of Association on club officials include restrictions on people who have been disqualified as a director "within the previous five years".
The inquiry team have also been charged with probing the financial revelations that have emerged in the last week, including the news that Rangers have failed to pay £9million in tax since Whyte took over last May.
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