Ten charities will receive grants, including Hospice UK which will offer individual grief trauma counselling to all front-line staff.
Catherine said the coronavirus pandemic "will have a lasting impact" on emergency responders' mental health.
The money will also help provide mental health support to schools.
The charity, the Royal Foundation, was initially set up in 2009 by Prince William and Prince Harry, and has focused on causes close to the princes' hearts, including the armed forces, conservation and mental health.
Catherine joined the charity after she became Duchess of Cambridge in 2011 and Meghan joined shortly before she and Harry were married in May 2018. Last year, Prince Harry and Meghan split from the foundation to forge their own charity.
During the coronavirus lockdown, the duke and duchess have been vocal about the need to look after people's mental health.
The £1.8m "Covid-19 Response Fund" will include grants to 10 charities: Mind, Hospice UK, the Ambulance Staff Charity, Campaign Against Living Miserably, Best Beginnings, The Anna Freud Centre, Place2Be, Shout 85258, The Mix, YoungMinds.
The ways the money will be used include:
All emergency responders will be able to get individual grief trauma counselling. Currently, Hospice UK's bereavement service originally provided counsellors for NHS England and social care staff, but it will be extended to all UK emergency services front-line workers
Mind's Blue Light programme - which ran from 2015 to 2019 and aimed to reduce stigma around mental health in ambulance, fire, police and search and rescue services - will be available to 250,000 emergency responders
Double the number of ambulance staff who may be struggling will be able to get support such as counselling or bereavement training through the Ambulance Staff Charity
Suicide prevention charity Campaign Against Living Miserably will increase capacity on its helplines, meaning they can respond to 2,300 more contacts each month
Online training and resources to help mental health will be provided to schools through Place2Be and the Anna Freud Centre
An extra 20,000 new mothers will be supported in a mental health training project led by Best Beginnings.
"Over recent months we have all been in awe of the incredible work that frontline staff and emergency responders have been doing in response to Covid-19, but we know that for many of them, their families, and for thousands of others across the UK, the pandemic will have a lasting impact on their mental health," said Catherine earlier this week, during a visit to speak to front-line workers and mental health counsellors.
William told them: "It's great to hear how The Royal Foundation is supporting you and many others to build resilience and give you the networks you need through its Covid-19 Response Fund, which will help ten leading charities continue their crucial work."
In May, during the lockdown, William warned of a potential mental health impact over hailing NHS workers as "heroes" during the coronavirus pandemic.
He said the praise could deter workers from seeking support as they feel pressure to appear "strong".
In a separate interview with the BBC, the couple said the lockdown is "stressful" for many people.
Psychiatrists have previously warned of a "tsunami" of mental illness from problems stored up during lockdown. They were particularly concerned that children and older adults are not getting the support they need because of school closures, self-isolation and fear of hospitals.
"We are already seeing the devastating impact of Covid-19 on mental health, with more people in crisis," said Prof Wendy Burn, president of the Royal College of Psychiatrists, at the end of May.
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