Officials from Operation Resolve asked the Crown Prosecution Service for advice on the consideration of charges against the force in December 2012.
In addition to corporate manslaughter, South Yorkshire Police were referred for consideration for offences contrary to the Health and Safety at Work Act 1974.
But a spokesman for Operation Resolve said neither charge could be pursued.
He said: “Prior to 1998, police officers were not subject to the application of the Health and Safety at Work Act and the legislation cannot be applied retrospectively.
“For a corporate manslaughter offence to be applicable to SYP it would need to be shown that the chief constable was personally grossly negligent in relation to the disaster.
“This cannot be proven in law in the circumstances relating to Hillsborough.”
Current South Yorkshire Police chief constable Stephen Watson said: “Decisions concerning the bringing of criminal charges are rightly for the CPS.
“Given that criminal proceedings are now active, it would be inappropriate for me to comment further for fear of jeopardising this important process in any way.
“In all of this however, our thoughts are with the Hillsborough families as we reflect on the appalling tragedy that is Hillsborough with the loss of so many innocent lives.”
No organisations have been charged with any offence in relation to Hillsborough, despite several being investigated.
The CPS said Sheffield Wednesday Football Club is now a “different company and as it is not a successor organisation, is not criminally liable for any offences that might have been committed”.
It said there was “insufficient evidence” and no realistic prospect of conviction against the Football Association for potential offences under the Safety of Sports Ground Act and the Health and Safety at Work Act.
No further action is to be taken against Sheffield City Council after being investigated under the same two acts.
The CPS said it could not prosecute the South Yorkshire Metropolitan Ambulance Service for legal reasons and there was insufficient evidence to bring charges against the two most senior employees of that organisation referred for consideration.
South Yorkshire police and crime commissioner Alan Billings said the modern-day force understands its operations must focus on victims.
In a statement he said: “Today’s announcement represents another milestone in the long history of the Hillsborough investigations.
“The start of criminal proceedings against these individuals will hopefully lead to a measure of closure for the family members who have experienced a long and traumatic process in their quest for justice and those officers who have lived under the shadow of the disaster for 28 years.
“I am reassured that South Yorkshire Police today understand very well that their present and future conduct has to be rooted in a commitment to uphold the values of public service and to putting the victim at the centre of their operation.”
A spokesman for Sheffield Wednesday said the club had no comment to make.