The move comes on the same day The Times reported that Glasgow's "super-hospital" was permitted to open despite the ventilation systems failing to meet the necessary safety standards.
Outbreaks of infection which are thought to have spread through the ventilation system at the Queen Elizabeth University Hospital (QEUH) have led to the deaths of two patients.
Ms Freeman and the Irish Health Minister, Simon Harris announced the initiative which will offer two three-month placements for Scottish and Irish senior policymakers or health service workers so they can learn more about what works in each system.
The pair are meeting in Dublin to mark the first anniversary of an existing learning exchange programme between Scottish and Irish health service workers to improve work on public health, patient safety and use of technology.
Addressing the Future Health – Opportunities for Collaboration symposium, Ms Freeman will say the initiative has gone from strength to strength and is a clear example of cooperation. The Health Secretary will also reiterate the Scottish Government’s serious concerns about the impact of Brexit on staffing in the health and social care sector.
READ MORE: Delayed discharges at Scottish hospitals hit more than 500,000 bed delaysHowever opposition parties were quick to criticise the move with the Scottish Conservatives saying it was time SNP ministers "got a grip" on the growing problems facing the NHS in Scotland and Social Care services.
Miles Briggs MSP Shadow Health Secretary said: “I welcome the launch of a joint Learning Fellowship programme between Scotland and Ireland.
“However given the many pressing issues facing our Scottish NHS from a major construction crisis in Lothian, Glasgow and Grampian on top of governance chaos in Tayside, a bullying crisis in the Highlands and financial fiascos in Ayrshire and Arran I’m surprised Jeane Freeman thinks it’s appropriate to drop what she’s doing and head to Ireland.
“I know Scottish patients and NHS staff desperate want to meet with Jeane Freeman to raise concerns and issues in person - they never get the opportunity to do that."
READ MORE: Inquiry into failings at new Sick Kids and Glasgow super-hospitalThe decision to open the QUEH is in stark contrast to Ms Freeman's last minute decision to postpone the transfer of patients to the new "Sick Kids" hospital in Edinburgh, which failed to meet the same ventilation standards.
The Scottish Irish Health Collaboration was established following a meeting in Dublin in October 2017 between the First Minister and the Taoiseach. At that meeting, health was identified as an area of particular interest for collaboration and learning and initial discussions began between Scottish and Irish officials in early 2018.
The goals of the Scottish Irish Health Collaboration are to - openly communicate information and ideas, deliberate on design and delivery issues and collaborate where appropriate opportunities exist.
Ms Freeman said: “Scotland and Ireland share a longstanding history, strengthened by trade and cultural links. The Scottish/Irish bilateral relationship today is as close as it has ever been and I am delighted to announce the Learning Fellowships. I am sure this exchange will benefit both jurisdictions.
“We collaborate on public policy areas ranging from social services to rural affairs, and in health our relationship is going from strength to strength.
“Of course, while we continue to develop our relationship with Ireland, we are doing so under the shadow of Brexit. With the ending of freedom of movement we know that in health, and in particular social care, we will be severely challenged in terms of our workforce.
“The Scottish Government wishes to make it clear that the efforts of EU staff within the NHS and social care sector are greatly appreciated. We want these workers to stay. Scotland is their home and we want it to continue being so.”