Dr Billings said on Wednesday he had no choice but to act “based on the erosion of public trust and confidence”.
He said: “I have been left with no choice other than to suspend David from his duties as chief constable of South Yorkshire police.
“I have reached this decision with a heavy heart following discussions with David.”
He had previously written online: “There is nothing that can do justice to the magnitude of the failure… We can only hope that these verdicts today contribute in some way to the healing that the grieving families need and that has been denied them for so long.”
Earlier, Andy Burnham, the shadow home secretary, described Mr Crompton’s position as “untenable”. The Labour MP, directly asked Theresa May in the Commons to consider the police chief’s position.
Law firm Broudie Jackson Canter, which represents several families at the inquest, said it welcome the suspension.
“We hope and expect that his conduct will be subject to the rigorous and impartial scrutiny which has so long been denied to the families,” a statement said.
Margaret Aspinall, the lead family campaigner, previously said: “This is on him. He should go, no doubt about it.”
Mr Crompton’s leadership has previously been drawn into question over the raid on Cliff Richard’s house in 2014 and the Rotherham child abuse ring.
Having already announced his notice of retirement in November, his immediate future is unclear regarding the disciplinary action.
The Home Office has also come under fire for signing a £19.4million cheque which helped officers, some of whom now face criminal charges, mount defences at the inquest.
But jurors threw out the statements on Tuesday, ruling supporters had not behaved in a way which was “unusually forceful or resistant to police control”.
The inquest had heard how Sgt Philip Lomas claimed he saw Liverpudlians carrying “carafes of wine” and “assumed” fans outside the turnstiles did not have tickets.