Sixteen people have been indicted in the scheme, including eight unlicensed brokers and their associates.
Four other people involved in the scheme, including one doctor, were arrested yesterday, the police said.
The charges cover the costs of running the scheme, including an awards ceremony at the end of the year.
The company said it would set out further details of the scheme, including a start date, soon.
A number of major employers have already pulled out of the scheme, including Waterstones, Sainsbury's and TK Maxx.
So far, seven schools have signed up for the scheme – including the private schools Eton and Wellington College.
Twelve other people were charged with smaller roles in the scheme, including posing as buyers or sellers, a job for which they were paid $500 apiece, prosecutors said.
The tycoon is thought to have offered to put £80m into the scheme, including £40m in cash and a £40m loan secured against BHS assets.
The lawyer accused a number of Russian officials as being behind the scheme, including Olga Stepanova, a senior tax official, and her husband Vladlen Stepanov.
Senior figures threw their weight behind the scheme, including Matthew Hancock and Nick Boles on the government side and Ed Miliband and Sadiq Khan from Labour.
The review will look at ways of increasing the flexibility and equality of the scheme, including in relation to benefits for unmarried partners.
