The couple will also not receive public funds for royal duties and will repay about $3 million Sovereign Grant funds they recently used to renovate their residence, Frogmore Cottage.
The new arrangement will take effect this spring, according to a statement from Buckingham Palace.
On Monday, senior royals held talks about the future roles for the couple.
"Harry, Meghan and Archie will always be much loved members of my family," said a statement from Queen Elizabeth released Saturday alongside Buckingham Palace's description of the new arrangement.
"I recognize 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," the Queen said.
Buckingham Palace said it would not comment on the details of security arrangements for the couple, who have said they intend to divide their time between Britain and North America.
The transition, like the couple's union, is unprecedented in modern royal history.
Markle, who is biracial with white and African-American family members, was born in the United States and worked as an actress before her marriage to Prince Harry.
She was best known for the USA Network series Suits, which was filmed in Toronto, and the couple is rumored to be considering a move to Canada after spending the holidays there with their 7-month-old son Archie.
In October, Markle said she had struggled with life as a new mother in the public eye.
Also in October, the couple sued Britain's Daily Mail over its decision to publish a private letter Markle wrote to her father shortly after her marriage, and Harry wrote that he saw his wife falling victim to the "same powerful forces" that had caused his mother's untimely death.