The couple will also no longer formally represent The Queen.
The Duke and Duchess of Sussex said they intend to repay £2.4m of taxpayer money for the refurbishment of Frogmore Cottage, which will remain their UK family home.
The new arrangement comes into effect in spring this year, the palace said.
The statement comes after senior royals held talks on Monday about the future role for the couple, who this month announced they wanted to “step back” as senior royals .
Queen’s statement on Harry and Meghan in full
The Harry and Meghan story
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 continued.
“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.