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In a statement released by Buckingham Palace, the couple said they plan to "carve out a progressive new role within this institution".
They said they intend to "work to become financially independent".
Last October, Prince Harry and Meghan publicly revealed their struggles under the media spotlight.
In their statement, also posted on their Instagram page, the couple said they made the decision "after many months of reflection and internal discussions".
"We intend to step back as 'senior' members of the Royal Family and work to become financially independent, while continuing to fully support Her Majesty The Queen.
"It is with your encouragement, particularly over the last few years, that we feel prepared to make this adjustment."
They said they plan to balance their time between the UK and North America while "continuing to honour our duty to the Queen, the Commonwealth, and our patronages".
"This geographic balance will enable us to raise our son with an appreciation for the royal tradition into which he was born, while also providing our family with the space to focus on the next chapter, including the launch of our new charitable entity."
Over Christmas, the couple took a break from royal duties to spend some time in Canada with their son, Archie, who was born in May.
The couple, together with their son Archie, recently spent time in Canada
After returning to the UK on Tuesday, Harry, 35, and Meghan, 38, visited Canada's High Commission in London to thank the country for hosting them and said the warmth and hospitality they received was "unbelievable".
During the visit, Meghan said it was "incredible time" to enjoy the "beauty of Canada".
"To see Archie go 'ah' when you walk by, and just see how stunning it is - so it meant a lot to us."
Former actress Meghan lived and worked in Toronto during her time starring in the popular US drama Suits.
Harry is sixth in line to the throne - behind Prince Charles, Prince William and his three children, but it is not clear what impact, if any, this announcement would have on the line of succession.
In an ITV documentary last year, Meghan admitted motherhood was a "struggle" due to intense interest from newspapers.
Prince Harry also responded to reports of a rift between him and his brother William, the Duke of Cambridge, by saying they were on "different paths".
In October, the duchess began legal action against the Mail on Sunday over a claim that it unlawfully published one of her private letters.
Prince Harry also released a statement, saying: "I lost my mother and now I watch my wife falling victim to the same powerful forces."
'Nothing like this in modern times'
Former Buckingham Palace press officer Dickie Arbiter suggested the decision showed Prince Harry's "heart ruling his head".
He told the BBC the "massive press onslaught" when their son Archie was born may have played a part in the decision.
And he compared the move to Edward VIII's abdication in 1936 in order to marry twice-divorced American Wallis Simpson.
"That is the only other precedent, but there's been nothing like this in modern times," he said.
Asked how being a "part-time" member of the Royal Family might work, he said he did not know.
"If they're going to be based in the UK, it means they are going to be doing a lot of flying (with) a big carbon footprint," he said, adding that this may "raise eyebrows".
