The Duke and Duchess of Sussex will also no longer formally represent The Queen, BBC reported on Saturday.
The couple will also repay £2.4 million of British taxpayers' money spent to renovate their UK family home, Frogmore Cottage.
The new arrangement comes into effect in spring this year, the palace said.
The development comes after senior members of the royal family held talks about the future role for the couple, who earlier this month announced they wanted to "step back" from their roles as senior royals.
The Queen said following "many months of conversations and more recent discussions" she was "pleased that together we have found a constructive and supportive way forward for my grandson and his family".
"Harry, Meghan and Archie will always be much loved members of my family," the statement said.
"I recognise the challenges they have experienced as a result of intense scrutiny over the last two years and support their wish for a more independent life.
"I want to thank them for all their dedicated work across this country, the Commonwealth and beyond, and am particularly proud of how Meghan has so quickly become one of the family.
"It is my whole family's hope that today's agreement allows them to start building a happy and peaceful new life."
The Buckingham Palace noted that they would continue to maintain their private patronages and associations.
"While they can no longer formally represent the Queen, the Sussexes have made clear that everything they do will continue to uphold the values of Her Majesty," the statement added.
Earlier this month, Harry and Meghan said they wanted a "progressive new role" within the institution, where they would be financially independent and divide their time between the UK and North America.
Last year, the couple spoke about the difficulties of royal life and media attention in recent months.
( With inputs from IANS )