Mr Drakeford who stood down in March after spending five years as First Minister, previously served as Health Minister between 2013-2016.
Ms Morgan also confirmed Huw Irranca-Davies in the role of Deputy First Minister in addition to his Climate Change and Rural Affairs Portfolio.
“As Deputy First Minister, Huw will support me in my role as First Minister and will work alongside me to deliver for the people for Wales,” said Ms Morgan.
“I have asked Mark Drakeford, Member for Cardiff West, to join the Ministerial team as Cabinet Secretary for Health and Social Care on an interim basis.
“Mark will bring his significant knowledge and experience to bear to continue our work to improve transparency and delivery.
“I have also today designated Elisabeth Jones under section 49(6) of the Government of Wales Act 2006 to exercise the functions of the Counsel General on an interim basis, in accordance with the provisions of that section.”
Mrs Jones was the Chief Legal Adviser for the National Assembly for Wales and Senedd from 2012 – 2019.
“The appointments I am announcing today will provide stability and continuity over the summer in the Ministerial team, complementing the changes announced on 17 July 2024.”
Further announcements on portfolio allocations will be made in September following a listening exercise over the summer with the Welsh public. This exercise will help to determine the Welsh Government’s priorities and the structure of government for the next 18 months.
Responding to Ms Morgan’s cabinet announcements, Welsh Conservative Senedd leader Andrew RT Davies said the “new government will be judged on their results”.
“What Wales needs is a government that can be a voice for all of Wales, and can deliver the NHS and the public services Wales deserves,” he said.
“After months of chaos in Welsh government, Wales will be watching.”
Plaid Cymru leader Rhun ap Iorwerth criticised Mr Drakeford’s appointment.
“At a time of crisis for the Welsh NHS, the last thing we need is an interim health minister that will only add to the uncertainty facing our health service,” he said.
“Wales deserves better than a government of stagnation and indecision.”
