Whyte has spoken out on the first anniversary of the club being plunged into administration.
Administrators Duff and Phelps were appointed on February 14 last year after HMRC lodged a petition over the non-payment of PAYE and VAT since Whyte's 2011 takeover.
The financial collapse of one of Scottish football's biggest clubs subsequently saw the Light Blues consigned to liquidation and voted into the Irn-Bru Third Division ahead of this season.
But, as far as Whyte is concerned, his conscience is clear following what has been a turbulent 12 months for Rangers.
He told Sky Sport News: "I welcome any fair investigation into anything to do with the takeover, the insolvency, whatever.
"I would welcome that and be happy to co-operate with any of it and anybody will see there is no wrong-doing whatsoever."
The Scottish businessman also denied any criminal activity during his time at Rangers.
He added: "If I was a crook or a wide-boy, do you really think I'm stupid enough to do anything remotely crooked at a high-profile football club?
"The whole notion is just utterly ridiculous."
Asked how he sleeps at night, Whyte replied: "Very soundly."
Meanwhile, Ibrox chief executive Charles Green believes Rangers have moved on from the trauma of the last 12 months.
Green headed the consortium which purchased the business and assets of the club when liquidation was confirmed last summer.
As well as benefiting from huge crowds at Ibrox this season, Rangers announced they had raised more than £22 million from their listing on the stock exchange in December.
Green told Rangers' official website: "As a club we are not just ready to move on - we have moved on.
"The successful flotation of the club on the Alternative Investment Market was the biggest single step on the road to recovery.
"The fact that our business could attract in excess of £22 million of investment in a challenging economic climate was heart-warming testament to the belief of investors from City institutions to individual fans.
"Shares have performed well and the capitalisation of the club has meant that we have very sound financial foundations for the future.
"No effort will be spared in pursuing avenues where our financial security can be developed and enhanced and we will be making announcements regarding this in due course.
"All along, we have known that the rebuilding of the club on the pitch will take time and we are prepared for that."
On the park, Rangers are out of all cup competitions this season but do sit 22 points clear at the top of the Third Division.
Boss Ally McCoist told Sky Sports News: "As a manager, I would probably say I would be content with where we are at the moment.
"Not overly happy and certainly not delirious but not too downbeat. By that I mean the lads have done very well in the league."