Previously, the couple shared photos on the account run by Kensington Palace which included photos of activities of Harry's elder brother Prince William and his family.
On Tuesday, @sussexroyal account went live.
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Last month, it was announced that as well as moving from London to Frogmore Cottage on the Windsor Estate to the west of the capital, the Duke and Duchess of Sussex, as Harry (34) and Meghan (37) are formally known, would be hiring an entirely new communications staff.
"Welcome to our official Instagram; we look forward to sharing the work that drives us, the causes we support, important announcements, and the opportunity to shine a light on key issues," the royal couple captioned their first post.
There has long been fascination with the British royal family, particularly in the United States, and the younger members such as Harry his elder brother Prince William (36) and their spouses are regularly greeted by large crowds.
Some two billion people were estimated to have watched the 2011 wedding of William, the first son of heir-to-the-throne Prince Charles and late wife Diana, to Catherine, the Duchess of Cambridge.
Tens of millions tuned in to see the marriage of William's brother Harry to US actress Meghan at Windsor Castle in May last year.
Harry and Meghan's first child, due soon, will be the seventh in line to the British throne.
