Hussey, 83, who served for decades as a lady in waiting to the late Queen Elizabeth II, resigned her honorary royal position after the incident.
The palace statement, issued on behalf of Hussey and Fulani, condemned the “appalling torrent of abuse on social media and elsewhere” directed at Fulani, and said it had been an “immensely distressing period” for both parties.
King Charles III and the royal family are pleased at the “welcome outcome,” the palace said.
Last year, Prince Harry’s wife Meghan, a biracial American, said a member of the royal household asked her what color skin her baby would have when she was pregnant with her first child.
Britain’s royal family is once again under intense scrutiny because of a six-part Netflix documentary about Harry and Meghan, in which the couple blame the royal household and the British media for their decision to quit royal duties in 2020 and move to California.