The independent inquiry into the circumstances surrounding the sacking of Carl Sargeant has been called off.
The Welsh Government will also pay the outstanding legal costs of the Sergeant family, following the inquest into the late AMs death.
Mr Sargeant was sacked from the cabinet by the then first minister Carwyn Jones in November 2017, over allegations of inappropriate behaviour with women.
The Alyn and Deeside AM took his own life days later.
The decision by the First Minister Mark Drakeford was welcomed by Mr Sargeant's family. "We must draw a line under everything and let our grieving process begin," they said.
Carwyn Jones had called the inquiry, and appointed barrister Paul Bowen to chair it, following the death of Mr Sargeant. The inquiry was to look into Mr Jones' actions before and after the dismissal.
It never got off the ground. The work stalled after the family of Mr Sargeant, unhappy at the format, began legal action. A High Court judge found it was unlawful that Mr Jones took decisions on the probe.
The coroner at Mr Sargeant's inquest later said that sacked ministers should be given more support.
After the inquest First Minister Mark Drakeford asked the chairman of ACAS, Sir Brendan Barber, to see if a way forward could be found between Mr Jones and Carl Sargeant's family.
Sir Brendan recommended that the investigation should not proceed, and that the Welsh Government should meet the outstanding legal costs of the Sargeant family for the inquest.
"I have decided to accept and to implement both," Mr Drakeford said.
"I know that all parties involved now share a wish to bring an end to the public controversy in relation to the tragic death of Carl, allowing us all to remember him as the valued husband, father, colleague and friend that he was."
In a statement, the family of Mr Sargeant said: "We have come to realise that the inquiry process would be unlikely to give us the answers we seek.
"So, enough is enough. We must draw a line under everything and let our grieving process begin. We also have no desire to distract the Welsh Government at a time of national crisis.
Neil Hudgell, the family's solicitor, said: "While feeling a great sense of frustration that answers to some questions will never be found, I hope they can now find some sense of closure in calling a halt to proceedings."
In correspondence published by the Welsh Government, Sir Brendan said that he felt the actions and decisions of the former first minister "have now been extensively scrutinised and questioned through the public processes of the coroners' inquest".
He said the family's judicial review and the inquiry proceedings costs have been met by the Welsh Government, but their costs for the inquest had not.
"It would seem wrong to me for this whole episode to be concluded with an ordinary family like the Sargeants to be at risk of being left with any significant outstanding legal bills," he said.
He said he has facilitated "exchanges" between Carwyn Jones and the family on his handling of the decisions the former first minister took.
"I hope these exchanges have been helpful to the family, but I well recognise that there will always I suspect remain a host of unanswered questions in their minds."
But Sir Brendan said both sides had a "strong wish" to move on from public discussion of Mr Sargeant's death and the "desperately unhappy circumstances surrounding that".
Mr Drakeford wrote he agreed with Sir Brendan that that the costs of the Bowen inquiry were not justifiable, and that the Welsh Government would make a payment of £220,000 to the Sargeant family, a figure Sir Brendan said would meet "all outstanding legal costs".
'Questions that simply have no answers'
In a statement, Carwyn Jones said: "This has been a traumatic time for everybody involved, particularly the family.
"With any tragedy of this kind, there will always be many questions that simply have no answers, but I am glad that they now have an opportunity to move on as best they can."
Welsh Conservative assembly leader Paul Davies said: "While I fully respect the agreement between the first minister and the Sargeant family it is clear that many questions remain unanswered and there is more information which could and should have been made available to them and assembly members for scrutiny."
Plaid Cymru Leader Adam Price added: "The wishes of the Sargeant family to bring this matter to a close must be respected and our thoughts continue to be with them.
"But it should never have taken this long for a decision to be made - and history will not look back kindly over the Welsh Government's handling of this case."