Lord William Nimmo Smith, who was one of five judges to hear the appeal of Abdelbaset Ali Mohmed al Megrahi's conviction for the Lockerbie bombing, will head the independent inquiry by Scottish football's governing body into the controversial takeover last year.
The former judge was called in by SFA chief executive Stewart Regan as it became increasingly frustrated by stalling tactics and obstructive behaviour from Whyte's solicitors.
Mr Regan said the inquiry team should establish whether Whyte has broken some of its Articles of Association and determine whether he meets the SFA's "fit and proper person" criteria.
An attempt will be made to interview Whyte himself before the inquiry team presents its findings within two weeks.
The panel will include Professor Niall Lothian OBE, a past president of the Institute of Chartered Accountants of Scotland. It also includes Bob Downes, former director with the BT Group and currently deputy chairman of the Scottish Environmental Protection Agency, and Mr Regan, who is a member of the panel in his capacity as an SFA director.
Mr Regan said the SFA was kept "at arm's length" by Rangers' solicitors. He said: "Despite our best endeavours to get information that would allow us to take a considered view, we just haven't had any information.
"We wanted to give the club every chance to explain the situation but that has been difficult. We decided that it now has to be escalated and we have asked for an independent inquiry with three, strong, high-profile individuals from the legal, financial and business communities.
"We believe the quality of these individuals will flush out the details we need to know and provide the board with whatever evidence we need to decide what happens next.
"Investigating allegations of unlawful or criminal activity is not a job for the SFA. Our panel is only looking at the SFA's Articles.
"If we do discover any information, we are duty bound to pass it on but so far there has been no transparency or disclosure [from Rangers]. That has made the SFA board determined to find out what has gone on at the club and then decide how we deal with that.
"It became clear they were being obstructive and unwilling to give us the information required."
He added: "We clearly were concerned at the stories that were emerging not just with Rangers, but the allegations against Mr Whyte. We decided that, having been held at arm's length from October to the end of January, enough was enough, and we had to launch an inquiry into what was going on.
"We made a number of requests to solicitors that were acting for Mr Whyte and had an exchange of correspondence going back to October. I don't know how many letters were involved but there were a lot and we were becoming frustrated at the obstructions being put in place to prevent us finding out information we needed."
The SFA wants to know more about why Whyte was banned from being a company director, between 2000 and 2007, which could contravene its rules on being a fit and proper person to hold office at a club. Officials who have breached SFA rules can be fined, suspended or subjected to other sanctions at the discretion of the governing body's Judicial Panel.
Mr Regan said Rangers could face punishment for Whyte's involvement, or their solicitors' refusal to fully co-operate, even if the owner leaves the club.
He added: "The Scottish FA still has power to hold the club to account. The club has an obligation to manage their directors and make sure their directors are behaving in a way that is fit for association with football."