Prince Harry and Meghan will lose royal funds and no longer use their HRH titles from spring, Buckingham Palace has confirmed.
The couple will be known as Harry, Duke of Sussex, and Meghan, Duchess of Sussex.
It mirrors the title taken by Diana, Princess of Wales, after her divorce.
Harry, who was born a prince of Wales, will remain a prince.
They will still use the property as their base when in the UK, but it is believed they will spend the majority of their time in North America.
They will keep their royal patronages as private patronages and associations, but Harry will be stepping down from his military appointments.
The announcement marks the conclusion of talks about their future with senior members of the family and royal aides.
The palace statement said: "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."
The Queen also issued a statement saying: "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.
"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."
Sky's royal correspondent Rhiannon Mills said: "In essence what we have this evening is a deal between the Sussexes and the rest of the family as to how exactly they can now start what they wanted which is this independent life.
"There are still clearly many details that need to be worked through but certainly this is beginning to give us a little more clarity."
Royal commentator Alastair Bruce said: "This is a seismic announcement from the Queen.
"This is an abdication in a sense from the Royal Family for Harry and he and his wife are now free, to a certain extent, to go and follow the dreams that they have."
The Sussexes website has been updated with the following: "In line with the statement by Her Majesty the Queen, information on the roles and work of the Duke and Duchess of Sussex will be updated on this website in due course.
"We appreciate your patience and invite you to explore the site to see the current works of Their Royal Highnesses."