The new development, due to be completed next year, will also include a 14-bed ready-to-go-home reablement unit, bringing NHS and social care teams together to support patients returning home after medical and surgical treatment in hospital.
Radiology services will be expanded, and four new dental suites built with increased training opportunities for dental nurses.
It is the first phase of a wider £60m investment in the hospital. A business case for the second phase, which would redevelop and improve the existing hospital buildings, is expected to be submitted by Betsi Cadwaladr University Health Board.
Plans to develop a new hospital on the Royal Alexandra site were first approved in 2013 but by 2018 estimated costs had doubled and the plans were halted during the Covid-19 pandemic.
Betsi Cadwaladr University Health Board said rising costs meant the original proposal was no longer affordable.