The investment was made by Aviva Investors through its REaLM infrastructure funds.
One of its clients, the UK Green Investment Bank (GIB) is indirectly investing £7.7 million into the £15.4m project.
The energy centre will provide 90% of the power and 100% of the heat for Ninewells.
LED lighting and insulation will be installed at Perth Royal Infirmary and Stracathro Hospital near Brechin as part of the project.
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The scheme is expected to cut energy costs by 10% at NHS Tayside.
A 25-year performance contract has been signed with Vital Energi, which was procured under the Carbon Energy Fund (CEF) framework.
Vital will be responsible for the design, construction, installation and on-going operation and maintenance of the technology for the duration of the contract.
The project is due for completion in December 2016.
Scotland Office minister Andrew Dunlop said: "This is an extremely welcome announcement as it combines enlightened investment with energy efficiency and the best of Scottish innovation. This centre will make a real difference to the costs of providing energy to hospitals in Tayside and is another example of UK institutional investors supporting infrastructure projects which will be of benefit to the wider public."
Mark Anderson, Head of Property, NHS Tayside, added: "This project is designed to make our hospital sites more energy efficient and enhance the service and environment for the patients and staff of NHS Tayside."
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