The project will remove asbestos, which was commonly used as fire retardant on structural steelworks in the 1970s when the hospital was built.
The aim is to ensure the hospital meets the latest fire and health and safety standards.
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The work also provides the opportunity to redesign and relocate a number of services and departments during the refurbishment, allowing the hospital to improve the quality of care.
The Minister made the announcement during a visit to Ysbyty Glan Clwyd.
Ms Griffiths said: "I am pleased to be able to give the final go-ahead today for the extensive work on Ysbyty Glan Clwyd. This work will improve the working environment for staff and provide better services for patients.
"This is a significant investment. The Welsh Government is committed to continued investment in the health service, and this announcement shows how we can do that despite the impact of cuts to the Welsh budget. I look forward to seeing the work progress."
(CD/GK)
