The Queen said in a statement: "Following many months of conversations and more recent discussions, I am 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.
"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."
Buckingham Palace said in a statement: "The Duke and Duchess of Sussex are grateful to Her Majesty and the Royal Family for their ongoing support as they embark on the next chapter of their lives.
"As agreed in this new arrangement, they understand that they are required to step back from Royal duties, including official military appointments.
"They will no longer receive public funds for Royal duties. With the Queen's blessing, the Sussexes will 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 Sussexes will not use their HRH titles as they are no longer working members of the Royal Family.
"The Duke and Duchess of Sussex have shared their wish to repay Sovereign Grant expenditure for the refurbishment of Frogmore Cottage, which will remain their UK family home. Buckingham Palace does not comment on the details of security arrangements.
"There are well established independent processes to determine the need for publicly funded security. This new model will take effect in the Spring of 2020."
