Staff at the centre were informed of the news in a meeting attended by the Tánaiste Simon Coveney, John Minihan and the Sisters of the Sacred Hearts of Jesus and Mary.
"All around the centre, everyone is delighted that services will continue to operate at Bessborough and jobs are secured," Pat Callanan of the Bessborough centre told.
The 40-acre estate in Blackrock accommodates community projects, which deliver a range of services to vulnerable families and children, including education programmes and employment supports.
These include specialised outreach family support service, The Lime Tree and the Family Access Programme, which supports supervised visitations for children to meet with family members.
Back in October, it was announced that up to 100 staff could be made redundant if the centre closed.
The statement issued by the Sisters of the Sacred Hearts of Jesus and Mary yesterday said the order will step down from the board of directors this summer.
"Previous announcements have referred to the transfer of the Bessborough Services to another service provider and the sale of lands at Bessborough," it read.
"We now wish to confirm that the Bessborough Centre Company Limited by Guarantee will continue the running of the services, including the creche, in full, with no impact on employment levels."
Ms Callanan said that the news came as a huge relief to staff after a tough number of months.
"Two people had bought houses just before we found out in October that we could be made redundant," she said, also stating that in the interim period, some staff had left because they feared the worst outcome.
"We had to stop taking on new referrals too because we didn't know the fate of the centre," she continued.
Ms Callanan said it will now be "full steam ahead" from Monday with the centre continuing to develop their services for children and families across Ireland.
It is expected that a recruitment drive will take place in the near future.
The Sisters of the Sacred Hearts of Jesus and Mary will step down from the Board of Directors by the end of June 2020 and be replaced by lay members.
The fate of the surrounding land around the centre is yet to be determined.
Lands on the site, part of which was a former mother and baby home, are of an extremely sensitive nature.
The order says they have co-operated fully with the Commission of Investigation.
Bessborough survivors and campaigners have called for the land to be preserved and protected.