The two officers were arrested on August 3 last year and an investigation led by Warwickshire Police named Operation Sacristy began.
The investigation into alleged corruption has seen both senior officers launch legal claims that they were wrongfully arrested. Both men strongly deny any wrong-doing.
In a statement shortly after their cases were referred to the CPS, Mr Price said: ''I am sure the public are concerned that we have been suspended on full pay for such a long time with no criminal charges being brought.
''I share that concern and frustration. I would much rather be back doing the job I love.''
Mr Bonnard said: ''I am determined to clear my name and return to work.
''I am at a loss as to why it is taking so long to deal with the criminal investigation.''
The IPCC said in a separate statement that the file it has passed on ''relates to conduct allegations made against Chief Constable Sean Price and Deputy Chief Constable Derek Bonnard''.
It added: ''The investigation was conducted under IPCC management by Keith Bristow, Director General (Designate) of the National Crime Agency.
''Mr Bristow is continuing with his separate criminal investigation, Operation Sacristy, into allegations against Mr Price, Mr Bonnard and others.
''In addition, an IPCC independent investigation into conduct allegations that Mr Price used undue influence to have an individual appointed to a role within the force has concluded and the report has been forwarded to Cleveland Police Authority.''
''I am at a loss as to why it is taking so long to deal with the criminal investigation.''
The IPCC said in a separate statement that the file it has passed on ''relates to conduct allegations made against Chief Constable Sean Price and Deputy Chief Constable Derek Bonnard''.
It added: ''The investigation was conducted under IPCC management by Keith Bristow, Director General (Designate) of the National Crime Agency.
''Mr Bristow is continuing with his separate criminal investigation, Operation Sacristy, into allegations against Mr Price, Mr Bonnard and others.
''In addition, an IPCC independent investigation into conduct allegations that Mr Price used undue influence to have an individual appointed to a role within the force has concluded and the report has been forwarded to Cleveland Police Authority.''