Prince Harry and his wife Meghan, also known as the Duke and Duchess of Sussex, have given up their Royal Highness titles and will no longer receive funds for public duties as they take a step back from the British monarchy.
The couple will also repay £2.4 million (Dh11.4m) in public funding that they were given to refurbish their cottage, Buckingham Palace said.
They will no longer represent formally Queen Elizabeth and will step back from royal duties, and will not be given official military appointments. Harry and Meghan will drop the title HRH, an acronym for His/Her Royal Highness, from their names.
"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," the Queen 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."
Her comments referred to battles with the media that prompted Harry and Meghan to sue several newspapers over intrusions into their private lives.
Queen Elizabeth said the couple and their son Archie would always be much loved members of her family.
"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," she said.
Royal expert and author Penny Junor said the new set-up would benefit both sides of the family.
"There are no blurred lines. They are starting afresh and they are going with the queen's blessing, I think it is the best of all worlds," she told AP.
She said it was the "best possible outcome" and one "which will actually avoid catastrophe".
"The country was so divided about this and so angry and so upset, so I think it was all a big mess and it was getting nastier by the day," she told the Daily Mail.
The announcement from Buckingham Palace on Saturday follows more than a week of intense private talks aimed at managing the fallout of the couple's shock decision to give up front-line royal duties.
Buckingham Palace said it would not comment on the family's security. They are expected to move to Canada.
Sky News's royal commentator Alastair Bruce said recent events had been an "enormous distraction and this is a seismic announcement from the queen".
"It's still very warm on the pastoral side of affection from a grandmother to her grandson and her great-grandson and granddaughter-in-law, but at the same time she has brought down the iron fist of monarchical leadership on a problem that needed to be solved," he said.