The Innovation Challenge, run by the National Endowment for Science, Technology and the Arts, known as Nesta, will fund innovative research ideas that can be developed into working ventures.
The first challenge will focus on managing chronic diseases, mental health and ageing. The Mental Health Foundation is leading a group of organisations that includes Mind, Rethink and the Sainsbury Centre for Mental Health to identify ways to break down the stigma of mental illness and improve standards of care.
Nesta is also working with the Young Foundation on a project that it hopes will speed up the formation of social enterprises in the health sector.
Jonathan Kestenbaum, chief executive of Nesta, called the project "the single biggest public call for imaginative ideas".
Ravi Kapur, head of innovation challenges at Nesta, said: "The third sector is the one that is most aware of where the innovation out there is at the moment."