Harry and Meghan will stop carrying out royal duties from the spring, will stop using HRH and will repay the taxpayers' millions spent on their Berkshire home.
The announcement marks the conclusion of talks about their future with senior members of the family and royal aides.
The Queen issued an emotional statement saying she recognised the "challenges" they had faced over the past year, adding: "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."
The couple's spokeswoman issued a statement on their behalf saying: "As agreed in this new arrangement, they understand that they are required to step back from royal duties, including official military appointments.
"They will no longer receive public funds for royal duties.
"With the Queen's blessing, the Sussexes will continue to maintain their private patronages and associations.
"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."