Prince Harry and Meghan will no longer use their HRH titles and will not receive public funds for royal duties, Buckingham Palace has announced.
The couple will also no longer formally represent the Queen.
The Duke and Duchess of Sussex intend to repay £2.4m of taxpayer money for the refurbishment of Frogmore Cottage, which will remain their UK family home, the statement added.
The new arrangement comes into effect in spring this year, the palace said.
The statement comes after the Queen held talks with the couple on Monday about their future, following their announcement that they wanted to "step back" 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 continued.
She thanked them for their "dedicated work", adding that she was "particularly proud of how Meghan has so quickly become one of the family."
In a separate statement, Buckingham Palace said: "The Sussexes will not use their HRH titles as they are no longer working members of the Royal Family."
HRH, an abbreviation of His/Her Royal Highness, is used as part of the title of some members of the royal family.
BBC royal correspondent Nicholas Witchell said: "There was a point when it seemed that they might have lost the HRH styling. They appear to have drawn back from that, because they simply won't use it.
"And I suspect that there may be a feeling in the palaces that perhaps at some point in the future they might come back."
Buckingham Palace said the duke and duchess understood they were required to step back from royal duties, including official military appointments.
"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," it said.
The statement added that the pair would continue to maintain their private patronages and associations.
Map Ives, director and founder of Rhino Conservation Botswana, said he had already been told by an official in Harry's office that the duke "wants to continue" his patronage of the organisation.
"If anything our relationship should get stronger," Mr Ives said.
There has been much speculation on who will provide security arrangements for the couple and how much it will cost, but the palace said it would not comment on such matters.
Harry and Meghan's new website, sussexroyal.com, was updated following the Queen's statement to say: "Information on the roles and work of the Duke and Duchess of Sussex will be updated on this website in due course."
The new post also invited visitors to the website to explore the site in the meantime to see the current works of "Their Royal Highnesses".
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, they both spoke about the difficulties of royal life and media attention.
The duke said he feared his wife would fall victim to "the same powerful forces" that led to his mother's death.
'Harder to think of a much cleaner break'
They will always be, the Queen writes, "much loved members of my family".
But that's about it. No royal title, no royal duties, no military appointments, no tours, most of their time spent in Canada, no public money.
It is harder to think of a much cleaner break than this. Harry and Meghan are still members of the Royal Family, but they are effectively no longer royal.
The early talk was of a much more mixed life - one where perhaps Harry and Meghan continued with some royal duties, dividing their time equally between the UK and Canada.
But the contradictions and conflicts of interest were too many.
There are still lots of details to thrash out.
And the whole thing will be reviewed after a year.
But a new life awaits Harry and Meghan - celebrities, certainly, but a different kind of royalty.
BBC royal correspondent Nicholas Witchell said questions remain unanswered from the statement, including what the couple's tax and immigration status will be in the UK and Canada.
Our correspondent said royal officials had not given a clear answer about whether Meghan still intended to gain British citizenship, which would entail her spending a certain amount of time in the UK.
He said that while they would divide their time between the UK and North America, it was expected that they will spend the majority of their time in North America.
Duncan Larcombe, former royal editor of the Sun and author of Prince Harry: The Inside Story, said a "scaled down Royal Family" had been "on the cards for some time".
"He is not going to be able to turn off that global fame. He still has an important role to play within the institution, that's probably why these discussions have dragged on a little bit longer than expected," he said.
Royal expert Penny Junor said the new arrangement was "the best possible outcome and an outcome which will actually avoid catastrophe".
She said: "They're hanging onto their patronages which I think is absolutely terrific because they both care passionately about making the world a better place."
However, she added: "The British public have lost out because these are two fantastic people who sprinkle fairy dust wherever they go and we are going to miss that, but clearly it was not making them happy."
Meghan and Harry have already begun a transition phase of living in Canada and the UK.
The move was agreed by the Queen, Prince of Wales and Duke of Cambridge.
The duchess is in the Commonwealth country with son Archie, where the Sussexes spent six weeks over the festive period.
On Tuesday she visited a charity in Vancouver which campaigns for teenage girls living in poverty.
On Thursday, the Duke of Sussex hosted the Rugby League World Cup draw at Buckingham Palace - his first public event since he and his wife said they would step back from royal life.
Compiled by Olalekan Adeleye