Hannah Black, 13, and Rochelle Cauvalt, 14, died after they lost their footing and were swept away by the stream at Stainforth Beck, near Settle, North Yorkshire.
The activity was part of a residential week planned by Royds school in Oulton, near Leeds.
The council will face two criminal charges for breaches of health and safety at work regulations at a preliminary hearing by Leeds magistrates on September 9.
Magistrates could impose a fine of up to pound;25,000 or refer the case to the Crown Court where fines are unlimited. Jail sentences cannot be imposed on council executives.
Neither the school nor the teachers who organised the trip will face charges. However its governing body is considering whether to take disciplinary action against any of the teachers involved.