Prince Harry also wants to prevent members of the armed forces from developing various types of mental illnesses such as post-traumatic stress disorder (PTSD), depression and anxiety.
Staying mentally and emotionally sharp could help with "getting that extra 20% or possibly 30% more of performance that can make all the difference", he said.
Since Harry left the military, he has made campaigning over mental health issues and the fate of veterans two of his priorities.
The money has come from their charitable trust, the Royal Foundation, and will be used to set up a digital innovation unit to develop new tools and services that will help people have conversations about their mental health and access support.
The joint initiative between the MoD and the Royal Foundation of the Duke and Duchess of Cambridge and Prince Harry comes days after the Foundation announced it will invest £2 million for the creation of a start-up company providing digital support to youngsters concerned about their mental well-being.
MoD said Monday's announcement will build upon a recently-launched United Kingdom government strategy aimed at improving mental health in current military workers, civilian staff their families and veterans.
"In the same way that someone might say they're going to give the gym a miss because they've got a slight strain, if we can get them talking about mental health problems at an early stage, then you don't let it fester".
Announcing the partnership, Sir Michael stressed the importance of mental health in a building a more effective armed forces. The former Royal Green Jacket said of his time in the armed forces: "We have to bear in mind, I was told this: "Grab a man suit and suck it up".
Jon White, a triple amputee former Royal Marines captain overseeing the project at the Royal Foundation, said troops would be shown an annual video featuring veterans and high-profile business people talking about mental fitness.
"That's what we're trying to create, this idea they can just speak about it the same way they do their physical fitness".