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 American 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."
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 a newspaper over a claim that it unlawfully published one of her private letters.
She accused the Mail on Sunday and its parent company of a campaign of "untrue" stories.