Whyte, who bought an 85 percent stake in the debt-laden club for a nominal one pound from David Murray last year, had to call in the administrators in February over unpaid taxes.
"The Crown Office has today instructed Strathclyde Police to conduct a criminal investigation into the acquisition of Rangers Football Club in May 2011 and the subsequent financial management of the club," Scottish prosecutors said in a statement on Monday.
"The investigation into alleged criminality follows a preliminary police examination of information passed to them in February this year by club administrators."
Rangers, one of the best supported clubs in British football, are now under new ownership but do not know which division they will be playing in next season.
The 54-times champions need the blessing of seven other clubs to be readmitted to the Scottish Premier League (SPL) after their parent company went into liquidation.
The 12-team SPL will make its decision on July 4. The BBC said four clubs had already come out against the readmission of Rangers - Hearts, Hibernian, Dundee United and Inverness Caledonian Thistle - meaning that another "No" would see them excluded.
It is not clear if Rangers would have to start life in the lowly third division or be relegated one notch to Scotland's first division.
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