Staff at Console are to be made redundant on Friday after a liquidator was appointed to the beleaguered charity.
The charity's services have been taken over by Pieta House, which will enter discussions with Console staff about offering them contracts.
The High Court earlier appointed a provisional liquidator to Console.
It was on the condition that the HSE could secure the handover of the charity's services to another provider.
Pieta House Chief Executive Officer, Brian Higgins, said: “Pieta House exists to serve people in crisis. We have a strong team at Pieta and will do everything possible to ensure that current users of the bereavement services will receive the same high quality service from Pieta House going forward.
"For us, it is also crucial to assure our existing clients, supporters and staff that there will be no impact on the counselling services that we currently offer to people in suicidal crisis and people who self-harm," he added.
Interim CEO of Console David Hall said: "There was no choice but to liquidate the company.
"Over the last few days I, with the HSE and Pieta House, have gone into extensive discussions to ensure the service will continue."
Here's what now former Interim CEO of @console_charity @davidhall75 on the changeover of services to @PietaHouse pic.twitter.com/jvuYPJofa0
— Sean Defoe (@SeanDefoe) July 14, 2016
As well as Console's 24-hour helpline, Pieta House will also take over the charity's Suicide Bereavement Liaison Service and its Suicide Bereavement Counselling Service.
The initial agreement with Pieta House will only last 10 days - a bridging agreement while they finalise details.
Console's helpline will be down for no more than an hour during the changeover, according to the HSE.
The HSE says all service users of Console will be individually contacted to ask if they want to transfer to Pieta House or opt out of the service.
There are 12 permanent and 60 part time staff and counsellors at Console.
In an affidavit, Mr Hall said the charity is 'hopelessly insolvent.'
He said it's almost €300,000 in debt - with €74,000 owed in wages and €77,500 due to the Revenue.
Mr Justice Gilligan said he was satisfied that the charity was hopelessly insolvent.
One of the main issues in the transfer is the security of private documents - and service users will be contacted to find out if they want their files transferred to a new service.
The case is due before the court again on July 28th.