Queen Elizabeth II said the agreement came together after “many months” of negotiations.
The two-hour family meeting was held to address the couple’s concerns.
“We have chosen to make a transition this year,” the pair said in a statement Wednesday.
The Mail on Sunday says it “will be defending this case vigorously.”
Prince Harry and Meghan Markle’s son was baptized Saturday at Windsor Castle.
The broadcaster said the tweet was “supposed to be a joke.”
Duke and Duchess of Sussex named their son Archie Harrison Mountbatten-Windsor.
The infant was born early Monday morning.
“Harry and Meghan: Becoming Royal” will premiere on May 27.
The Duke and Duchess of Sussex’s baby is due next spring.