Mr Green was charged after arriving at Livingston police station.
Mr Whyte later attended a police station in Glasgow and was detained in custody.
A third man, former Rangers co-administrator David Whitehouse, was earlier arrested in England.
All three men are expected to appear at Glasgow Sherriff Court on Wednesday.
Craig Whyte, 44, took over Rangers in May 2011. The club entered administration the following year.
Charles Green led the consortium which bought Rangers assets in 2012 following the club's liquidation.
But he stepped down from Rangers a year later following allegations that he was working in conjunction with Craig Whyte.
A police spokesman said: "Police Scotland can confirm a 44-year-old man has been arrested and is presently detained in police custody in connection with an ongoing investigation into an alleged fraudulent acquisition of Rangers FC in 2012.
"A report will be submitted to the procurator fiscal."
An earlier police statement said a 62-year-old man had been arrested and detained over the same investigation.
Arriving at the police station on Tuesday morning, Mr Green, 62, said: "I've been invited to attend an interview with Police Scotland. I have done that on a number of occasions in the past."
Asked why he was there, Mr Green replied: "Well, one of the difficulties with today is my legal people had asked Police Scotland to provide us information that we're likely to be questioned on and they wouldn't provide that so I'm at a loss really."
David Whitehouse, 50, who worked for administrators Duff and Phelps, had earlier been arrested in connection with the 2012 acquisition.
Police said in a statement: "Following a Police Scotland operation on Tuesday, a 50-year-old man has been arrested in connection with the ongoing investigation into the alleged fraudulent acquisition of Rangers FC in 2012.
"Around 6am officers from Police Scotland's economic crime unit, assisted by officers from Cheshire, attended at an address in England and detained the 50-year-old man.
"He has now been arrested and is presently detained in police custody."

Financial Fraud Action UK (FFA UK) said there had been a particular rise in the scam in the last few weeks.
Several small or medium-sized companies in the UK have lost sums of between Â£10,000 and Â£20,000 as a result.
Typically, staff in a firm's finance department receive an email, which they believe is from a senior manager.
The fraudsters use special software to make the message appear genuine.
The emails request that urgent payments are made outside normal procedures, often for a pressing reason, such as the need to secure a contract.
The scam has been dubbed "whaling" fraud, as it targets the so-called big fish of business.
When the money is transferred, it goes into an account set up by the fraudsters.
"While an urgent request from the boss might naturally prompt a swift response, it should in fact be a warning sign of a potential scam," said Katy Worobec, director of FFA UK.
Staff are being advised to:
Former Rangers owner Craig Whyte and ex-chief executive Charles Green have been arrested as part of an inquiry into the "alleged fraudulent acquisition" of the club in 2012.
[NEXT_CONCEPT]
Office staff are being warned about fake emails that appear to come from one of their bosses, telling them to transfer money.